algorithm - highest weighted path for multiple destinations -

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i have directed cyclic weighted graph. want find path highest of weights, in length of x vertices, , don't care destination. want find highest cost.

this can solved via dynamical-programming-like algorithm.

as have few hundreds of nodes , x round 10. can assign each node v array fv size x, , fv[i] represents maximum cost source node v length i.

let s source. set fs[0] = 0, , other fs[i] = -infinity.

all other arrays initialized -infinity array.

now,

for each node v, following update:

fv[i] = max{fv[i], fw[i-1] + cost(w, v) | w neighbor of v}

repeat above updates @ least x times, , check fv[x] v maximum possible value want.

you can use information retrieve path, should easy do.

above algorithm special case of bellman-ford algorithm


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