A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs
نویسندگان
چکیده
We consider the problem of computing a minimum cycle basis in a directed graph G with m arcs and n vertices. The arcs of G have non-negative weights assigned to them. We give an Õ(mn) algorithm, which is the first polynomial time algorithm for this problem. We also present an Õ(mn) randomized algorithm. The problem of computing a minimum cycle basis in an undirected graph has been well-studied. However, it is not known if an efficient algorithm for undirected graphs automatically translates to an efficient algorithm for directed graphs.
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An Õ(m2n) Randomized Algorithm to Compute a Minimum Cycle Basis of a Directed Graph
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