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Finding a cheapest
cycle in a quasi-transitive digraph with real-valued vertex costs
J. Bang-Jensen, G. Gutin and A. Yeo
Disrete Optimization
Volume 3,
,
2004.
AbstractWe consider the problem of finding a minimum cost cycle in a
digraph with real-valued costs on the vertices. This problem
generalizes the problem of finding a longest
cycle and hence is NP-hard for
general digraphs. We prove that the problem is solvable in
polynomial time for extended semicomplete digraphs and for
quasi-transitive digraphs, thereby generalizing a number of
previous results on these classes. As a byproduct of our method we
develop polynomial algorithms for the following problem: Given a
quasi-transitive digraph $D$ with real-valued vertex costs, find,
for each $j=1,2,\ldots{},|V(D)|$, $j$ disjoint paths
$P_1,P_2,\ldots{},P_j$ such that the total cost of these paths is
minimum among all collections of $j$ disjoint paths in $D$. [Edit]
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