Othon Michail's Publications

Publications of Othon Michail

This is a compressed list with links to abstracts and pdfs. Also available as a BibTex file.

All papers on this site may be downloaded for research or personal use only. The copyright for each paper is owned either by the publisher of the journal or conference proceedings in which the paper is published, or by the authors of the paper.

Monographs

New Models for Population Protocols,
with Ioannis Chatzigiannakis and Paul Spirakis.
Synthesis Lectures on Distributed Computing Theory,
Nancy Lynch edt., Morgan & Claypool Publishers, 2011.
[bib]

@Book{ MCS11,
	title = "New Models for Population Protocols",
	booktitle = "New Models for Population Protocols",
	author = "Othon Michail and Ioannis Chatzigiannakis and Paul G. Spirakis",
	publisher = "Morgan \& Claypool",
	series = "N. A. Lynch (Ed), Synthesis Lectures on Distributed Computing Theory",
	year = "2011",
	editor = "Nancy A. Lynch",
}

Book Chapters

Connectivity Preserving Network Transformers,
with Paul Spirakis.
In Emergent Computation,
Edited by A. Adamatzky, pages 337-359, Springer, 2016.
[PDF] [bib] [Abstract]

The Population Protocol model is a distributed model that concerns systems of very weak computational entities that cannot control the way they interact. The model of Network Constructors is a variant of Population Protocols capable of (algorithmically) constructing abstract networks. Both models are characterized by a \emph{fundamental inability to terminate}. In this work, we investigate the minimal strengthenings of the latter model that could overcome this inability. Our main conclusion is that \emph{initial connectivity of the communication topology} combined with the ability of the protocol to \emph{transform the communication topology} and the ability of a node to \emph{detect when its degree is equal to a small constant}, plus either a \emph{unique leader} or the ability of \emph{detecting common neighbors}, are sufficient to guarantee not only \emph{termination} but also the \emph{maximum computational power that one can hope for in this family of models}. In particular, the model, under these minimal assumptions, \emph{computes with termination any symmetric predicate computable by a Turing Machine of space $\Theta(n^2)$.
```
@InBook{ MS16e,
	title = "Emergent Computation",
	author = "Othon Michail and Paul G. Spirakis",
	editor = "A. Adamatzky",
	publisher = "Springer",
	chapter = "Connectivity Preserving Network Transformers",
        pages = "337--359",
	year = "2016"
}
   
```
Computing in Dynamic Networks,
with Ioannis Chatzigiannakis and Paul Spirakis.
In Computational Network Theory: Theoretical Foundations and Applications, First Edition,
Edited by M. Dehmer, F. Emmert-Streib, and S. Pickl, pages 173-218, Wiley-VCH Verlag GmbH & Co. KGaA, 2015.
[PDF] [bib] [Abstract]

In this chapter, our focus is on computational network analysis from a theoretical point of view. In particular, we study the \emph{propagation of influence and computation in dynamic distributed computing systems}. We focus on a \emph{synchronous message passing} communication model with bidirectional links. Our network dynamicity assumption is a \emph{worst-case dynamicity} controlled by an adversary scheduler, which has received much attention recently. We first study the fundamental \emph{naming} and \emph{counting} problems (and some variations) in networks that are \emph{anonymous}, \emph{unknown}, and possibly dynamic. Network dynamicity is modeled here by the \emph{1-interval connectivity model}, in which communication is synchronous and a (worst-case) adversary chooses the edges of every round subject to the condition that each instance is connected. We then replace this quite strong assumption by minimal \emph{temporal connectivity} conditions. These conditions only require that \emph{another causal influence occurs within every time-window of some given length}. Based on this basic idea we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate \emph{termination criteria} in networks in which an upper bound on any of these metrics is known. We exploit these termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental \emph{counting} and \emph{all-to-all token dissemination} (or \emph{gossip}) problems. Finally, we propose another model of worst-case temporal connectivity, called \emph{local communication windows}, that assumes a fixed underlying communication network and restricts the adversary to allow communication between local neighborhoods in every time-window of some fixed length. We prove some basic properties and provide a protocol for counting in this model.
```
@InBook{ MCS15,
	title = "Computational Network Theory: Theoretical Foundations and Applications, First Edition",
	author = "Othon Michail and Ioannis Chatzigiannakis and Paul G. Spirakis",
	editor = "M. Dehmer and F. Emmert-Streib and S. Pickl",
	publisher = "Wiley-VCH Verlag GmbH \& Co. KGaA",
	chapter = "Computing in Dynamic Networks",
        pages = "173--218",
	year = "2015"
}
   
```
Population Protocols and Related Models,
with Ioannis Chatzigiannakis and Paul Spirakis.
In Theoretical Aspects of Distributed Computing in Sensor Networks,
S. Nikoletseas and J. Rolim edt., Springer-Verlag, 2010.
Remark: The editors decided to include only P. Spirakis in the author index.
My name and the name of I. Chatzigiannakis appear in the abstract.
[PDF] [bib] [Abstract]

This is a joint work with Ioannis Chatzigiannakis and Othon Michail. We discuss here the population protocol model and most of its well-known extensions. The population protocol model aims to represent sensor networks consisting of tiny computational devices with sensing capabilities that follow some unpredictable and uncontrollable mobility pattern. It adopts a minimalistic approach and, thus, naturally computes a quite restricted class of predicates and exhibits almost no fault tolerance. Most recent approaches make extra realistic and implementable assumptions, in order to gain more computational power and/or speedup the time to convergence and/or improve fault tolerance. In particular, the mediated population protocol model, the community protocol model, and the PALOMA model, which are all extensions of the population protocol model, are thoroughly discussed. Finally, the inherent difficulty of verifying the correctness of population protocols that run on complete communication graphs is revealed, but a promising algorithmic solution is presented.
```
@InBook{ CMS10-2,
	title = "Theoretical Aspects of Distributed Computing in Sensor Networks",
	author = "Paul G. Spirakis",
	editor = "S. Nikoletseas and J. Rolim",
	publisher = "Springer-Verlag",
	chapter = "Population Protocols and Related Models",
	year = "2010"
}
   
```

Journals and Conferences

How Many Cooks Spoil the Soup?
with Paul Spirakis.
In 23rd International Colloquium on Structural Information and Communication Complexity
(SIROCCO), pages 3-18, Helsinki, Finland, July 2016.
[SIROCCO] [Presentation] [Arxiv] [bib] [Abstract]

In this work, we study the following basic question: \emph{``How much parallelism does a distributed task permit?''} Our definition of \emph{parallelism} (or \emph{symmetry}) here is not in terms of speed, but in terms of identical \emph{roles} that processes have at the same time in the execution. For example, we may ask: \emph{``Can a given task be solved by a protocol that always has at least two processes in the same role at the same time?''} (i.e. by a protocol that never elects a \emph{unique leader}). We choose to initiate this study in population protocols, a very simple model that not only allows for a straightforward definition of what a role is, but also encloses the challenge of isolating the properties that are due to the protocol from those that are due to the \emph{adversary scheduler}, who controls the interactions between the processes. In particular, we define the role of a process at a given time to be equivalent to the \emph{state} of the process at that time. Moreover, we isolate the symmetry that is due to the protocol (\emph{inherent symmetry}) by focusing on those schedules that maximize symmetry for that protocol and observing how much symmetry breaking the protocol is forced to achieve in order to solve the problem. To allow for such \emph{symmetry maximizing} schedules we consider \emph{parallel schedulers} that in every step may select a whole collection of pairs of nodes (up to a perfect matching) to interact and not just a single pair. Based on these definitions of symmetric computation, we (i) give a \emph{partial characterization} of the set of predicates on input assignments that can be \emph{stably computed with maximum symmetry}, i.e. $\Theta(N_{min})$, where $N_{min}$ is the minimum multiplicity of a state in the initial configuration, and (ii) we turn our attention to the remaining predicates (that have some essentially different properties) and prove a \emph{strong impossibility result} for the \emph{parity} predicate: the inherent symmetry of any protocol that stably computes it is \emph{upper bounded by a constant that depends on the size of the protocol}.
```
@inproceedings{MS16d,
  title={How Many Cooks Spoil the Soup?},
  author={Michail, Othon and Spirakis, Paul G},
  booktitle={Proceedings of the 23rd International Colloquium on Structural Information and Communication Complexity (SIROCCO)},
  year={2016},
  location = {Helsinki, Finland},
  isbn = {978-3-319-48313-9},
  pages = {3--18},
  numpages = {16},
  url = {http://link.springer.com/chapter/10.1007%2F978-3-319-48314-6_1},
  doi = {10.1007/978-3-319-48314-6_1},
  publisher = {Springer}
}
   
```
Connectivity Preserving Network Transformers,
with Paul Spirakis.
Theoretical Computer Science (TCS), Special Issue on the Theory of Self-Assembly, Elsevier,
2016, doi: 10.1016/j.tcs.2016.02.040.
[TCS] [Arxiv] [bib] [Abstract]

The Population Protocol model is a distributed model that concerns systems of very weak computational entities that cannot control the way they interact. The model of Network Constructors is a variant of Population Protocols capable of (algorithmically) constructing abstract networks. Both models are characterized by a \emph{fundamental inability to terminate}. In this work, we investigate the minimal strengthenings of the latter model that could overcome this inability. Our main conclusion is that \emph{initial connectivity of the communication topology} combined with the ability of the protocol to \emph{transform the communication topology} and the ability of a node to \emph{detect when its degree is equal to a small constant}, plus either a \emph{unique leader} or the ability of \emph{detecting common neighbors}, are sufficient to guarantee not only \emph{termination} but also the \emph{maximum computational power that one can hope for in this family of models}. The technique of our protocols is to transform any initial connected topology to a \emph{less symmetric} (that can serve as a large ordered memory) and \emph{detectable} (that the protocol can determine its successful construction) topology \emph{without ever breaking its connectivity} during the transformation. The target topology of all of our transformers is the \emph{spanning line} and we call \emph{Terminating Line Transformation} the corresponding problem. We first study the case in which there is a pre-elected \emph{unique leader} and give a \emph{time-optimal protocol for Terminating Line Transformation}. We then prove that dropping the leader without additional assumptions leads to a \emph{strong impossibility result}. In an attempt to overcome this, we equip the nodes with the ability to tell, during their pairwise interactions, whether they have at least one neighbor in common. Interestingly, it turns out that this local and realistic mechanism is sufficient to make the problem solvable. In particular, we give a \emph{very efficient protocol} that solves Terminating Line Transformation when all nodes are initially identical. The latter implies the aforementioned strong characterization: \emph{the model, under a few minimal assumptions, computes with termination any symmetric predicate computable by a Turing Machine of space $\Theta(n^2)$.}
```
@article{MS16c,
  title={Connectivity Preserving Network Transformers},
  author={Michail, Othon and Spirakis, Paul G},
  journal={Theoretical Computer Science},
  year={2016},
  issn = {0304-3975},
  doi = {http://dx.doi.org/10.1016/j.tcs.2016.02.040},
  url = {http://www.sciencedirect.com/science/article/pii/S0304397516002024},
  publisher={Elsevier}
}
   
```
An Introduction to Temporal Graphs: An Algorithmic Perspective.
Internet Mathematics, 12(4), 239-280, Taylor & Francis, June 2016.
A previous version appeared in
Algorithms, Probability, Networks, and Games - Scientific Papers and Essays Dedicated to
Paul G. Spirakis on the Occasion of His 60th Birthday, pages 308-343, LNCS, Springer, 2015.
[IM] [APNG] [bib] [Abstract]

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed as a sequence $G_1,G_2\ldots,G_l$ of static graphs over the same (static) set of nodes $V$. Though static graphs have been extensively studied, for their temporal generalization we are still far from having a concrete set of structural and algorithmic principles. Recent research shows that many graph properties and problems become radically different and usually substantially more difficult when an extra time dimension is added to them. Moreover, there is already a rich and rapidly growing set of modern systems and applications that can be naturally modeled and studied via temporal graphs. This, further motivates the need for the development of a temporal extension of graph theory. We survey here recent results on temporal graphs and temporal graph problems that have appeared in the Computer Science community.
```
@article{Mi16
 author = {Michail, Othon},
 title = {An Introduction to Temporal Graphs: An Algorithmic Perspective},
 journal = {Internet Mathematics},
 volume = {12},
 number = {4},
 pages = {239--280},
 year = {2016},
 issn = {1542-7951},
 doi = {http://dx.doi.org/10.1080/15427951.2016.1177801},
 url = {http://www.tandfonline.com/doi/full/10.1080/15427951.2016.1177801},
 publisher = {Taylor \& Francis}
}
   
```
Terminating Distributed Construction of Shapes and Patterns in a Fair Solution of Automata.
In 34th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC),
pages 37-46, Donostia-San Sebastián, Spain, July 2015.
[PODC] [Presentation] [Arxiv] [bib] [Abstract]

In this work, we consider a \emph{solution of automata} similar to \emph{Population Protocols} and \emph{Network Constructors}. The automata, also called \emph{nodes}, move passively in a well-mixed solution and can \emph{cooperate} by interacting in pairs. During every such interaction, the nodes, apart from updating their states, may also choose to connect to each other in order to start forming some required structure. The model introduced here is a more applied version of Network Constructors, imposing \emph{geometrical constraints} on the permissible connections. Each node can connect to other nodes only via a very limited number of \emph{local ports}, which implies that at any given time it has only a \emph{bounded number of neighbors}. Connections are always made at \emph{unit distance} and are \emph{perpendicular to connections of neighboring ports}. Though this variation can no longer form abstract networks, it is still capable of forming very practical \emph{2D or 3D shapes}. We develop \emph{new techniques} for determining the computational and constructive capabilities of our model. One of the main novelties, concerns our attempt to overcome the inherent inability of such systems to terminate. In particular, exploiting the assumptions that the system is well-mixed and has a unique leader, we \emph{give terminating protocols that are correct with high probability} (w.h.p.). This allows us to develop terminating subroutines that can be \emph{sequentially composed} to form larger \emph{modular protocols}. One of our main results is a \emph{terminating protocol counting the size $n$ of the system} w.h.p.. We then use this protocol as a subroutine in order to develop our \emph{universal constructors}, establishing that \emph{it is possible for the nodes to self-organize w.h.p. into arbitrarily complex shapes and additionally always terminate}.
```
@inproceedings{Mi15,
 author = {Michail, Othon},
 title = {Terminating Distributed Construction of Shapes and Patterns in a Fair Solution of Automata},
 booktitle = {Proceedings of the 34th ACM Symposium on Principles of Distributed Computing (PODC)},
 year = {2015},
 location = {Donostia-San Sebasti{\'a}n, Spain},
 isbn = {978-1-4503-2944-6},
 pages = {37--46},
 numpages = {10},
 url = {http://doi.acm.org/10.1145/2767386.2767402},
 doi = {10.1145/2767386.2767402},
 acmid = {2767402},
 publisher = {ACM}
}
   
```
Traveling Salesman Problems in Temporal Graphs,
with Paul Spirakis.
Theoretical Computer Science (TCS), 634, 1-23, Elsevier, June 2016.
A previous version appeared in
39th International Symposium on Mathematical Foundations of Computer Science (MFCS),
pages 553-564, Budapest, Hungary, August 2014.
[TCS] [MFCS] [Presentation] [bib] [Abstract]

In this work, we introduce the notion of time to some well-known combinatorial optimization problems. In particular, we study problems defined on \emph{temporal graphs}. A temporal graph $D=(V,A)$ may be viewed as a time-sequence $G_1,G_2,\ldots,G_l$ of static graphs over the same (static) set of nodes $V$. Each $G_t=D(t)=(V,A(t))$ is called the \emph{instance of $D$ at time $t$} and $l$ is called the \emph{lifetime of $D$}. Our main focus is on analogues of \emph{traveling salesman problems} in temporal graphs. A sequence of time-labeled edges (e.g. a tour) is called \emph{temporal} if its labels are strictly increasing. We begin by considering the problem of exploring the nodes of a temporal graph as soon as possible. In contrast to the positive results known for the static case, we prove that, it cannot be approximated within $cn$, for some constant $c>0$, in a special case of temporal graphs and within $(2-\varepsilon)$, for every constant $\varepsilon>0$, in another special case in which $D(t)$ is strongly connected for all $1\leq t\leq l$, both unless $\rem{P}=\rem{NP}$. We then study the temporal analogue of TSP(1,2), abbreviated TTSP(1,2), where, for all $1\leq t\leq l$, $D(t)$ is a complete weighted graph with edge-costs from $\{1,2\}$ and the cost of an edge may vary from instance to instance. The goal is to find a minimum cost temporal TSP tour. We give several \emph{polynomial-time approximation algorithms} for TTSP(1,2). Our best approximation is $(1.7+\varepsilon)$ for the generic TTSP(1,2) and $(13/8+\varepsilon)$ for its interesting special case in which the lifetime of the temporal graph is restricted to $n$. In the way, we also introduce temporal versions of other fundamental combinatorial optimization problems, for which we obtain polynomial-time approximation algorithms and hardness results.
```
@article{MS16b,
 author = {Michail, Othon and Spirakis, Paul G.},
 title = {Traveling Salesman Problems in Temporal Graphs},
 journal = {Theoretical Computer Science},
 volume = {634},
 pages = {1--23},
 year = {2016},
 issn = {0304-3975},
 doi = {http://dx.doi.org/10.1016/j.tcs.2016.04.006},
 url = {http://www.sciencedirect.com/science/article/pii/S0304397516300342},
 publisher = {Elsevier}
}
   
```
Simple and Efficient Local Codes for Distributed Stable Network Construction,
with Paul Spirakis.
Distributed Computing, 29(3), 207-237, Springer, June 2016.
A previous version appeared in
33rd Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC),
pages 76-85, Paris, France, July 2014.
[DC] [PODC] [Presentation] [bib] [Abstract]

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction, we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol. Moreover, we assume pairwise interactions between the processes that are scheduled by a fair adversary. In order to allow processes to construct networks, we let them activate and deactivate their pairwise connections. When two processes interact, the protocol takes as input the states of the processes and the state of their connection and updates all of them. Initially all connections are inactive and the goal is for the processes, after interacting and activating/deactivating connections for a while, to end up with a desired stable network. We give protocols (optimal in some cases) and lower bounds for several basic network construction problems such as spanning line, spanning ring, spanning star, and regular network. The expected time to convergence of our protocols is analyzed under a uniform random scheduler. Finally, we prove several universality results by presenting generic protocols that are capable of simulating a Turing Machine (TM) and exploiting it in order to construct a large class of networks. We additionally show how to partition the population into k supernodes, each being a line of log k nodes, for the largest such k. This amount of local memory is sufficient for the supernodes to obtain unique names and exploit their names and their memory to realize nontrivial constructions.
```
@article{MS16a,
 author = {Michail, Othon and Spirakis, Paul G.},
 title = {Simple and efficient local codes for distributed stable network construction},
 journal = {Distributed Computing},
 volume = {29},
 number = {3},
 pages = {207--237},
 year = {2016},
 issn = {0178-2770},
 doi = {http://dx.doi.org/10.1007/s00446-015-0257-4},
 pages = {1-31},
 url = {https://link.springer.com/article/10.1007/s00446-015-0257-4},
 publisher = {Springer Berlin Heidelberg}
}
   
```
Naming and Counting in Anonymous Unknown Dynamic Networks,
with Ioannis Chatzigiannakis and Paul Spirakis.
In 5th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS),
pages 281-295, Osaka, Japan, November 2013.
Also as brief announcement in 26th International Symposium on DIStributed Computing (DISC),
pages 437-438, Salvador, Brazil, October 2012.
[SSS] [Presentation] [DISC] [Arxiv] [bib] [Abstract]

In this work, we study the fundamental naming and counting problems (and some variations) in networks that are anonymous, unknown, and possibly dynamic. In counting, nodes must determine the size of the network n and in naming they must end up with unique identities. By anonymous we mean that all nodes begin from identical states apart possibly from a unique leader node and by unknown that nodes have no a priori knowledge of the network (apart from some minimal knowledge when necessary) including ignorance of n. Network dynamicity is modeled by the 1-interval connectivity model [KLO10], in which communication is synchronous and a (worst-case) adversary chooses the edges of every round subject to the condition that each instance is connected. We first focus on static networks with broadcast where we prove that, without a leader, counting is impossible to solve and that naming is impossible to solve even with a leader and even if nodes know n. These impossibilities carry over to dynamic networks as well. We also show that a unique leader suffices in order to solve counting in linear time. Then we focus on dynamic networks with broadcast. We conjecture that dynamicity renders nontrivial computation impossible. In view of this, we let the nodes know an upper bound on the maximum degree that will ever appear and show that in this case the nodes can obtain an upper bound on n. Finally, we replace broadcast with one-to-each, in which a node may send a different message to each of its neighbors. Interestingly, this natural variation is proved to be computationally equivalent to a full-knowledge model, in which unique names exist and the size of the network is known.
```
@inproceedings{MCS13b,
  title={Naming and counting in anonymous unknown dynamic networks},
  author={Michail, Othon and Chatzigiannakis, Ioannis and Spirakis, Paul G},
  booktitle={15th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)},
  pages={281--295},
  year={2013},
  publisher={Springer}
}
   
```
Temporal Network Optimization Subject to Connectivity Constraints,
with George Mertzios, Ioannis Chatzigiannakis, and Paul Spirakis.
In 40th International Colloquium on Automata, Languages and Programming (ICALP),
pages 657-668, Riga, Latvia, July 2013.
[ICALP] [Presentation] [Arxiv] [bib] [Abstract]

In this work we consider temporal networks, i.e. networks defined by a labeling $\lambda$ assigning to each edge of an underlying graph G a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by $\lambda$ a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.
```
@inproceedings{MMCS13,
  title={Temporal Network Optimization Subject to Connectivity Constraints},
  author={Mertzios, George B and Michail, Othon and Chatzigiannakis, Ioannis and Spirakis, Paul G},
  booktitle={40th International Colloquium on Automata, Languages and Programming (ICALP)},
  pages={663--674},
  year={2013},
  volume={7966},
  number={Part 2},
  series={Lecture Notes in Computer Science},
  month={July},
  publisher={Springer}
}
   
```
Causality, Influence, and Computation in Possibly Disconnected Synchronous Dynamic Networks,
with Ioannis Chatzigiannakis and Paul Spirakis.
Journal of Parallel and Distributed Computing (JPDC), 74(1), 2016-2026, Elsevier, January 2014.
A previous version appeared in
16th International Conference On Principles Of DIstributed Systems (OPODIS),
pages 269-283, Rome, Italy, December 2012.
[JPDC] [OPODIS] [Presentation] [bib] [Abstract]

In this work, we study the propagation of influence and computation in dynamic distributed computing systems that are possibly disconnected at every instant. We focus on a synchronous message-passing communication model with broadcast and bidirectional links. Our network dynamicity assumption is a worst-case dynamicity controlled by an adversary scheduler, which has received much attention recently. We replace the usual (in worst-case dynamic networks) assumption that the network is connected at every instant by minimal temporal connectivity conditions. Our conditions only require that another causal influence occurs within every time window of some given length. Based on this basic idea, we define several novel metrics for capturing the speed of information spreading in a dynamic network. We present several results that correlate these metrics. Moreover, we investigate termination criteria in networks in which an upper bound on any of these metrics is known. We exploit our termination criteria to provide efficient (and optimal in some cases) protocols that solve the fundamental counting and all-to-all token dissemination (or gossip) problems.
```
@article{MCS14,
  title={Causality, influence, and computation in possibly disconnected synchronous dynamic networks},
  author={Michail, Othon and Chatzigiannakis, Ioannis and Spirakis, Paul G},
  journal={Journal of Parallel and Distributed Computing},
  volume={74},
  number={1},
  pages={2016--2026},
  year={2014},
  publisher={Elsevier}
}
   
```

Myriads of data, myriads of devices: self-awareness of the Ad-hoc,
with Ioannis Chatzigiannakis, Georgios Mylonas, and Paul Spirakis.
Awareness: Self-Awareness in Autonomic Systems, November 2012.
[PDF] [bib]

@article{CMMS12,
  title={Myriads of data, myriads of devices: self-awareness of the Ad-hoc},
  author={Chatzigiannakis, Ioannis and Michail, Othon and Mylonas, Georgios and Spirakis, Paul},
  journal={Awareness: Self-Awareness in Autonomic Systems},
  year={2012}
}

Terminating Population Protocols via some Minimal Global Knowledge Assumptions,
with Paul Spirakis.
Journal of Parallel and Distributed Computing (JPDC), 81-82, 1-10, Elsevier, July 2015.
A previous version (also with I. Chatzigiannakis) appeared in
14th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS),
pages 77-89, Toronto, Canada, October 1-4, 2012.
[JPDC] [SSS] [Presentation] [bib] [Abstract]

We extend the population protocol model with a cover-time service that informs a walking state every time it covers the whole network. This represents a known upper bound on the cover time of a random walk. The cover-time service allows us to introduce termination into population protocols, a capability that is crucial for any distributed system. By reduction to an oracle-model we arrive at a very satisfactory lower bound on the computational power of the model: we prove that it is at least as strong as a Turing Machine of space log n with input commutativity, where n is the number of nodes in the network. We also give a log n-space, but nondeterministic this time, upper bound. Finally, we prove interesting similarities of this model to linear bounded automata.
```
@article{MS15,
  title={Terminating population protocols via some minimal global knowledge assumptions},
  author={Michail, Othon and Spirakis, Paul G},
  journal={Journal of Parallel and Distributed Computing},
  volume={81},
  pages={1--10},
  year={2015},
  publisher={Elsevier}
}
   
```
The Computational Power of Simple Protocols for Self-Awareness on Graphs,
with Ioannis Chatzigiannakis, Stavros Nikolaou, and Paul Spirakis.
Theoretical Computer Science (TCS),
Special Issue on Stabilization, Safety, and Security of Distributed Systems 2011 (SSS),
512, 98-118, Elsevier, November 2013.
A previous version appeared in
13th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS),
pages 135-147, Grenoble, France, October 10-12, 2011.
[TCS] [SSS] [Presentation] [bib] [Abstract]

We explore the capability of a network of extremely limited computational entities to decide properties about itself or any of its subnetworks. We consider that the underlying network of the interacting entities (devices, agents, processes etc.) is modeled by an interaction graph that reflects the network’s connectivity. We examine the following two cases: First, we consider the case where the input graph is the whole interaction graph and second where it is some subgraph of the interaction graph given by some preprocessing on the network. In each case, we devise simple graph protocols that can decide properties of the input graph. The computational entities, that are called agents, are modeled as finite-state automata and run the same global graph protocol. Each protocol is a fixed size grammar, that is, its description is independent of the size (number of agents) of the network. This size is not known by the agents. We present two simple models (one for each case), the Graph Decision Mediated Population Protocol (GDMPP) and the Mediated Graph Protocol (MGP) models, similar to the Population Protocol model of Angluin et al., where each network link (edge of the interaction graph) is characterized by a state taken from a finite set. This state can be used and updated during each interaction between the corresponding agents. We provide some example protocols and some interesting properties for the two models concerning the computability of graph languages in various settings (disconnected input graphs, stabilizing input graphs). We show that the computational power within the family of all (at least) weakly-connected input graphs is fairly restricted. Finally, we give an exact characterization of the class of graph languages decidable by the MGP model in the case of complete interaction graphs: it is equal to the class of graph languages decidable by a nondeterministic Turing Machine of linear space that receives its input graph by its adjacency matrix representation.
```
@article{CMNS13,
  title={The computational power of simple protocols for self-awareness on graphs},
  author={Chatzigiannakis, Ioannis and Michail, Othon and Nikolaou, Stavros and Spirakis, Paul G},
  journal={Theoretical Computer Science},
  volume={512},
  pages={98--118},
  year={2013},
  publisher={Elsevier}
}
   
```
Passively Mobile Communicating Machines that Use Restricted Space,
with Ioannis Chatzigiannakis, Stavros Nikolaou, Andreas Pavlogiannis, and Paul Spirakis.
Theoretical Computer Science (TCS), 412(46), 6469-6483, Elsevier, 2011.
A previous version appeared in
7th ACM SIGACT/SIGMOBILE International Workshop on Foundations of Mobile Computing (FOMC),
San Jose, California, USA, June 9, 2011.
[TCS] [FOMC] [Presentation] [bib] [Abstract]

We propose a new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model [Angluin et al. 2006] is that agents now, instead of being automata, are Turing Machines. We provide general definitions for unbounded memories, but we are mainly interested in computations upper-bounded by plausible space limitations. However, we prove that our results hold for more general cases. We focus on \emphcomplete interaction graphs and define the complexity classes PMSPACE(f(n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f(n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f(n)) when f(n) = Ω(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf(n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are Ω(log n). We next explore the computability of the PM model when the protocols use o(loglog n) space per machine and prove that SEM = PMSPACE(f(n)) when f(n) = o(loglog n), where SEM denotes the class of the semilinear predicates. Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n).
```
@article{MNPS11,
  author    = {Ioannis Chatzigiannakis and
               Othon Michail and
               Stavros Nikolaou and
               Andreas Pavlogiannis and
               Paul G. Spirakis},
  title     = {Passively mobile communicating machines that use restricted
               space},
  journal   = {Theoretical Computer Science},
  volume    = {412},
  number    = {46},
  year      = {2011},
  pages     = {6469-6483},
  month     = {October},
  ee        = {http://dx.doi.org/10.1016/j.tcs.2011.07.001}
}
   
```
Algorithmic Verification of Population Protocols,
with Ioannis Chatzigiannakis, and Paul Spirakis.
In 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS),
pages 221-235, New York City, USA, September 20-22, 2010.
[SSS] [Presentation] [bib] [Abstract]

In this work, we study the Population Protocol model of Angluin et al. from the perspective of protocol verification. In particular, we are interested in algorithmically solving the problem of determining whether a given population protocol conforms to its specifications. Since this is the first work on verification of population protocols, we redefine most notions of population protocols in order to make them suitable for algorithmic verification. Moreover, we formally define the general verification problem and some interesting special cases. All these problems are shown to be NP-hard. We next propose some first algorithmic solutions for a natural special case. Finally, we conduct experiments and algorithmic engineering in order to improve our verifiers’ running times.
```
@InProceedings{ CMS10,
	author = "Ioannis Chatzigiannakis and Othon Michail and Paul G. Spirakis",
	title = "Algorithmic verification of population protocols",
	booktitle = "12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)",
	year = "2010",
	volume = "6366",
	series = "Lecture Notes in Computer Science",
	pages = "221--235",
	month = "September",
	publisher = "Springer-Verlag",
	location = "New York City, USA"
}
   
```
Stably Decidable Graph Languages by Mediated Population Protocols,
with Ioannis Chatzigiannakis, and Paul Spirakis.
In 12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS),
pages 252-266, New York City, USA, September 20-22, 2010.
Also as: Brief Announcement: Decidable Graph Languages by Mediated Population Protocols,
in 23rd International Symposium on DIStributed Computing (DISC),
pages 239-240, Elche, Spain, Sept. 2009.
[SSS] [Presentation] [DISC] [bib] [Abstract]

We work on an extension of the Population Protocol model of Angluin et al. that allows edges of the communication graph, G, to have states that belong to a constant size set. In this extension, the so called Mediated Population Protocol model (MPP), both uniformity and anonymity are preserved. We study here a simplified version of MPP in order to capture MPP’s ability to stably compute graph properties. To understand properties of the communication graph is an important step in almost any distributed system. We prove that any graph property is not computable if we allow disconnected communication graphs. As a result, we focus on studying (at least) weakly connected communication graphs only and give several examples of computable properties in this case. To do so, we also prove that the class of computable properties is closed under complement, union and intersection operations. Node and edge parity, bounded out-degree by a constant, existence of a node with more incoming than outgoing neighbors, and existence of some directed path of length at least TeX are some examples of properties whose computability is proven. Finally, we prove the existence of symmetry in two specific communication graphs and, by exploiting this, we prove that there exists no protocol, whose states eventually stabilize, to determine whether G contains some directed cycle of length 2.
```
@InProceedings{ CMS10-3-1,
	author = "Ioannis Chatzigiannakis and Othon Michail and Paul G. Spirakis",
	title = "Stably Decidable Graph Languages by Mediated Population Protocols",
	booktitle = "12th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)",
	year = "2010",
	volume = "6366",
	series = "Lecture Notes in Computer Science",
	pages = "252--266",
	month = "September",
	publisher = "Springer-Verlag",
	location = "New York City, USA"
}
   
```
Computational Models for Wireless Sensor Networks: A Survey,
with Apostolos Filippas, Stavros Nikolaou, Andreas Pavlogiannis, Ioannis Chatzigiannakis, and Paul Spirakis.
In 1st International Conference for Undergraduate and Postgraduate Students in Computer Engineering,
Informatics, related Technologies and Applications (EUREKA!),
Ancient Olympia, Greece, 14-16 October, 2010.
[PDF] [bib] [Abstract]

Here we survey various computational models for Wireless Sensor Networks (WSNs). The population protocol model (PP) considers networks of tiny mobile finite-state artifacts that can sense the environment and communicate in pairs to perform a computation. The mediated population protocol model (MPP) enhances the previous model by allowing the communication links to have a constant size buffer, providing more computational power. The graph decision MPP model (GDM) is a special case of MPP that focuses on the MPP’s ability to decide graph properties of the network. Another direction towards enhancing the PP is followed by the PALOMA model in which the artifacts are no longer finite-state automata but Turing Machines of logarithmic memory in the population size. A different approach to modeling WSNs is the static synchronous sensor field model (SSSF) which describes devices communicating through a fixed communication graph and interacting with their environment via input and output data streams. In this survey, we present the computational capabilities of each model and provide directions for further research.
```
@InProceedings{ FNPMCS10,
	author = "Apostolos Filippas and Stavros Nikolaou and Andreas Pavlogiannis and Othon Michail and Ioannis Chatzigiannakis and Paul G. Spirakis",
	title = "Computational Models for Wireless Sensor Networks: A Survey",
	booktitle = "1st International Conference for Undergraduate and Postgraduate Students in Computer Engineering, Informatics, related Technologies and Applications (EUREKA!)",
	year = "2010",
	note = "Also FRONTS Technical Report, FRONTS-TR-2010-18, \url{http://fronts.cti.gr/aigaion/?TR=156}",
	location = "Ancient Olympia, Greece"
}
   
```
All Symmetric Predicates in NSPACE(n^2) are Stably Computable by the Mediated Population Protocol Model,
with Ioannis Chatzigiannakis, Stavros Nikolaou, Andreas Pavlogiannis, and Paul Spirakis.
In 35th International Symposium on Mathematical Foundations of Computer Science (MFCS),
pages 270-281, Brno, Czech Republic, August 23-27, 2010.
[MFCS] [Presentation] [bib] [Abstract]

This work focuses on the computational power of the Mediated Population Protocol model on complete communication graphs and initially identical edges (SMPP). In particular, we investigate the class MPS of all predicates that are stably computable by the SMPP model. It is already known that MPS is in the symmetric subclass of NSPACE(n^2). Here we prove that this inclusion holds with equality, thus, providing the following exact characterization for MPS: A predicate is in MPS iff it is symmetric and is in NSPACE(n^2).
```
@InProceedings{ CMNPS10-2,
	author = "Ioannis Chatzigiannakis and Othon Michail and Stavros Nikolaou and Andreas Pavlogiannis and Paul G. Spirakis",
	title = "All symmetric predicates in ${NSPACE}(n^2)$ are stably computable by the mediated population protocol model",
	booktitle = "35th International Symposium on Mathematical Foundations of Computer Science (MFCS)",
	year = "2010",
	volume = "6281",
	series = "Lecture Notes in Computer Science",
	pages = "270--281",
	month = "August 23--27",
	publisher = "Springer-Verlag",
	location = "Brno, Czech Republic"
}
   
```
Computational Models for Networks of Tiny Artifacts: a Survey,
with Carme Alvarez, Ioannis Chatzigiannakis, Amalia Duch, Joaquim Gabbaro, Maria Serna, and Paul Spirakis.
Computer Science Review (CSR), 5(1), 7-25, Elsevier, May 2010.
[CSR] [bib] [Abstract]

We survey here some recent computational models for networks of tiny artifacts. In particular, we focus on networks consisting of artifacts with sensing capabilities. We first imagine the artifacts moving passively, that is, being mobile but unable to control their own movement. This leads us to the population protocol model of [Angluin et al. 2004]. We survey this model and some of its recent enhancements. In particular, we also present the mediated population protocol model in which the interaction links are capable of storing states and the passively mobile machines model in which the finite state nature of the agents is relaxed and the agents become multitape Turing machines that use a restricted space. We next survey the sensor field model, a general model capturing some identifying characteristics of many sensor network's settings. A sensor field is composed of kinds of devices that can communicate one to the other and also to the environment through input/output data streams. We, finally, present simulation results between sensor fields and population protocols and analyze the capability of their variants to decide graph properties.
```
@Article{ ACMSS10,
	author = "Carme {\`A}lvarez and Ioannis Chatzigiannakis and Amalia Duch and Joaquim Gabarr{\'o} and Othon Michail and Serna Maria and Paul G. Spirakis",
	title = "Computational Models for Networks of Tiny Artifacts: A Survey",
	journal = "Computer Science Review",
	year = "2011",
	volume = "5",
	number = "1",
	month = "January",
	doi = "doi:10.1016/j.cosrev.2010.09.001"
}
   
```
On the Fairness of Probabilistic Schedulers for Population Protocols,
with Ioannis Chatzigiannakis, Shlomi Dolev, Sandor Fekete, and Paul Spirakis.
In Algorithmic Methods for Distributed Cooperative Systems,
Dagstuhl Seminar Proceedings, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany, 2010.
[PDF] [Presentation] [bib] [Abstract]

We propose a novel, generic definition of emph{probabilistic schedulers} for population protocols. We design two new schedulers, the emph{State Scheduler} and the emph{Transition Function Scheduler}. Both possess the significant capability of being emph{protocol-aware}, i.e. they can assign transition probabilities based on information concerning the underlying protocol. We prove that the proposed schedulers, and also the emph{Random Scheduler} that was defined by Angluin et al. [2004], are all fair with probability $1$. We also define and study emph{equivalence} between schedulers w.r.t. emph{performance} and emph{correctness} and prove that there exist fair probabilistic schedulers that are not equivalent w.r.t. to performance and others that are not equivalent w.r.t. correctness. We implement our schedulers using a new tool for simulating population protocols and evaluate their performance from the viewpoint of experimental analysis and verification. We study three representative protocols to verify stability, and compare the experimental time to convergence with the known complexity bounds. We run our experiments from very small to extremely large populations (of up to $10^{8}$ agents). We get very promising results both of theoretical and practical interest.
```
@InProceedings{CDFMS10,
  author =	{Ioannis Chatzigiannakis and Shlomi Dolev and S{\'a}ndor Fekete and Othon Michail and Paul Spirakis},
  title =	{On the Fairness of Probabilistic Schedulers for Population Protocols},
  booktitle =	{Algorithmic Methods for Distributed Cooperative Systems},
  year =	{2010},
  editor =	{S{\'a}ndor Fekete and Stefan Fischer and Martin Riedmiller and Suri Subhash},
  number =	{09371},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2428},
  annote =	{Keywords: Population Protocols, Fairness, Probabilistic Schedulers, Communicating Automata, Sensor Networks, Experimental Evaluation}
}
   
```
Not All Fair Probabilistic Schedulers are Equivalent,
with Ioannis Chatzigiannakis, Shlomi Dolev, Sandor Fekete, and Paul Spirakis.
In 13th International Conference On Principles Of DIstributed Systems (OPODIS),
pages 33-47, Nimes, France, December 15-18, 2009.
[OPODIS] [Presentation] [bib] [Abstract]

We propose a novel, generic definition of probabilistic schedulers for population protocols. We then identify the consistent probabilistic schedulers, and prove that any consistent scheduler that assigns a non-zero probability to any transition i -> j, where i and j are configurations satisfying i \neq j, is fair with probability 1. This is a new theoretical framework that aims to simplify proving specific probabilistic schedulers fair. In this paper we propose two new schedulers, the State Scheduler and the Transition Function Scheduler. Both possess the significant capability of being protocol-aware, i.e. they can assign transition probabilities based on information concerning the underlying protocol. By using our framework we prove that the proposed schedulers, and also the Random Scheduler that was defined by Angluin et al. [2], are all fair with probability 1. Finally, we define and study equivalence between schedulers w.r.t. performance and correctness and prove that there exist fair probabilistic schedulers that are not equivalent w.r.t. to performance and others that are not equivalent w.r.t. correctness.
```
@InProceedings{ CDFMS09,
	author = "Ioannis Chatzigiannakis and Shlomi Dolev and S{\'a}ndor P. Fekete and Othon Michail and Paul G. Spirakis",
	title = "Not All Fair Probabilistic Schedulers Are Equivalent",
	booktitle = "13th International Conference on Principles of Distributed Systems (OPODIS)",
	year = "2009",
	volume = "5923",
	series = "Lecture Notes in Computer Science",
	pages = "33--47",
	publisher = "Springer-Verlag",
	doi = "http://dx.doi.org/10.1007/978-3-642-10877-8\\\\\\\\\\_5",
	isbn = "978-3-642-10876-1",
	location = "N\^{\i}mes, France"
}
   
```
Recent Advances in Population Protocols,
with Ioannis Chatzigiannakis and Paul Spirakis.
In 34th International Symposium on Mathematical Foundations of Computer Science (MFCS),
invited talk of Paul Spirakis, pages 56-76, Novy Smokovec, High Tatras, Slovak Republic, 2009 .
[MFCS] [Presentation] [bib] [Abstract]

The population protocol model (PP) proposed by Angluin et al. [2] describes sensor networks consisting of passively mobile finite-state agents. The agents sense their environment and communicate in pairs to carry out some computation on the sensed values. The mediated population protocol model (MPP) [13] extended the PP model by communication links equipped with a constant size buffer. The MPP model was proved in [13] to be stronger than the PP model. However, its most important contribution is that it provides us with the ability to devise optimizing protocols, approximation protocols and protocols that decide properties of the communication graph on which they run. The latter case, suggests a simplified model, the GDM model, that was formally defined and studied in [11]. GDM is a special case of MPP that captures MPP’s ability to decide properties of the communication graph. Here we survey recent advances in the area initiated by the proposal of the PP model and at the same time we provide new protocols, novel ideas and results.
```
@InProceedings{ CMS09-2,
	author = "Ioannis Chatzigiannakis and Othon Michail and Paul G. Spirakis",
	title = "Recent Advances in Population Protocols",
	booktitle = "34th International Symposium on Mathematical Foundations of Computer Science (MFCS)",
	year = "2009",
	volume = "5734",
	series = "Lecture Notes in Computer Science",
	pages = "56--76",
	address = "Berlin, Heidelberg",
	publisher = "Springer-Verlag",
	doi = "http://dx.doi.org/10.1007/978-3-642-03816-7\\\\\\\\\\_6",
	isbn = "978-3-642-03815-0",
	location = "Novy Smokovec, High Tatras, Slovakia"
}
   
```
Mediated Population Protocols,
with Ioannis Chatzigiannakis and Paul Spirakis.
Theoretical Computer Science (TCS), 412(22), 2434-2450, Elsevier, February 2011.
Based on two previous versions:
(i) In 36th International Colloquium on Automata, Languages and Programming (ICALP),
pages 363-374, Rhodes, Greece, July, 2009.
(ii) see MFCS 2010 above.
[TCS] [ICALP] [Presentation] [bib] [Abstract]

We extend here the Population Protocol (PP) model of Angluin et al. (2004, 2006) [2,4] in order to model more powerful networks of resource-limited agents that are possibly mobile. The main feature of our extended model, called the Mediated Population Protocol (MPP) model, is to allow the edges of the interaction graph to have states that belong to a constant-size set. We then allow the protocol rules for pairwise interactions to modify the corresponding edge state. The descriptions of our protocols preserve both the uniformity and anonymity properties of PPs, that is, they do not depend on the size of the population and do not use unique identifiers. We focus on the computational power of the MPP model on complete interaction graphs and initially identical edges. We provide the following exact characterization of the class MPS of stably computable predicates: a predicate is in MPS iff it is symmetric and is in NSPACE(n^2).
```
@Article{ MCS11-2,
	author = "Othon Michail and Ioannis Chatzigiannakis and Paul G. Spirakis",
	title = "Mediated population protocols",
	journal = "Theoretical Computer Science",
	issue_date = "May, 2011",
	volume = "412",
	number = "22",
	month = "May",
	year = "2011",
	issn = "0304-3975",
	pages = "2434--2450",
	numpages = "17",
	url = "http://dx.doi.org/10.1016/j.tcs.2011.02.003",
	doi = "http://dx.doi.org/10.1016/j.tcs.2011.02.003",
	acmid = "1967853",
	publisher = "Elsevier Science Publishers Ltd.",
	address = "Essex, UK",
	keywords = "Diffuse computation, Finite-state agent, Intermittent communication, Passive mobility, Population protocol, Stable computation"
}
   
```
Improving the Integration of Neuro-Symbolic Rules with Case-Based Reasoning,
with Jim Prentzas and Ioannis Hatzilygeroudis.
In 5th Hellenic conference on Artificial Intelligence: Theories, Models and Applications (SETN),
pages 377-382, 2008.
[bib] [Abstract]

In this paper, we present an improved approach integrating rules, neural networks and cases, compared to a previous one. The main approach integrates neurules and cases. Neurules are a kind of integrated rules that combine a symbolic (production rules) and a connectionist (adaline unit) representation. Each neurule is represented as an adaline unit. The main characteristics of neurules are that they improve the performance of symbolic rules and, in contrast to other hybrid neuro-symbolic approaches, they retain the modularity of production rules and their naturalness in a large degree. In the improved approach, various types of indices are assigned to cases according to different roles they play in neurule-based reasoning, instead of one. Thus, an enhanced knowledge representation scheme is derived resulting in accuracy improvement. Experimental results demonstrate its effectiveness.
```
@InProceedings{ PHM08,
year={2008},
isbn={978-3-540-87880-3},
booktitle={Artificial Intelligence: Theories, Models and Applications},
volume={5138},
series={Lecture Notes in Computer Science},
editor={Darzentas, John and Vouros, GeorgeA. and Vosinakis, Spyros and Arnellos, Argyris},
doi={10.1007/978-3-540-87881-0_36},
title={Improving the Integration of Neuro-Symbolic Rules with Case-Based Reasoning},
url={http://dx.doi.org/10.1007/978-3-540-87881-0_36},
publisher={Springer Berlin Heidelberg},
author={Prentzas, Jim and Hatzilygeroudis, Ioannis and Michail, Othon},
pages={377-382},
language={English}
}
   
```

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