**L**et's assume a network ** G** with cost function for its sides

- There are no arcs for a peak to itself,therefore
*e**(**ii*does not belong to the*)***E**set for**i=1..n**.As usually,**n**is the number of the peaks of.*G* - All costs are positive,therefore
*c**[e**(**ij**)**]***>0**for**i<>j.** - We expand the
function to the non existing sides(*c**e**(**ii*not belonging to the*)***E**set for**i=1..n)**assuming that : - The cost of the direct access of one peak to itself is zero,
*c**[e**(**ii**)*=0;*]* - If there is no side connecting
*V*to*(i)**V*that is*(j)**e**(**ij*does not belong to the E set,then the direct access from one peak to another costs infinite.The final conclusion is:*)*^{c[e(ij)] }^{=}**{**^{ }**0 , if i=j**.**infinite , if i<>j.**

We can easily assume that ** G** is

As cost of a ** G's** undergraph is set the total cost of its sides.We are extremely concerned in the
cost of a genetic tree

We will examine two algorithms,which solve the problem of finding the ** minimum genetic tree
(m.g.t.) **that is a genetic tree T which satisfies the following:

They are the

(You obviously click on the algorithm you wish to learn more about.)

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