A correctness certificate for the Stoer–Wagner min-cut algorithm

Autor: Srinivasa R. Arikati, Kurt Mehlhorn
Rok vydání: 1999
Předmět:
Zdroj: Information Processing Letters. 70:251-254
ISSN: 0020-0190
DOI: 10.1016/s0020-0190(99)00071-x
Popis: The Stoer‐Wagner algorithm computes a minimum cut in a weighted undirected graph. The algorithm works inn 1 phases, wheren is the number of nodes ofG. Each phase takes time O.mCn logn/ ,w herem is the number of edges ofG, and computes a pair of vertices s and t and a minimum cut separatings and t . We show how to extend the algorithm such that each phase also computes a maximum flow from s tot . The flow is computed in O.m/ additional time and certifies the cut computed in the phase. © 1999 Elsevier Science B.V. All rights reserved. We give a correctness certificate for the min-cut algorithm of Stoer and Wagner [6]. This algorithm refines the algorithm of Nagamochi and Ibaraki [5,4]; it has the same time complexity, but is simpler. The algorithm is deterministic. There are faster randomized algorithms [2,3]. No certificates are known for the randomized algorithms. Let G be an undirected graph with n vertices and m edges. The algorithm of Stoer and Wagner works inn 1 phases. In each phase it identifies two vertices and a minimum cut separating them and then collapses the two vertices into one. The global min-cut is the minimum cut found in any phase. Each phase runs in time O.mCn logn/. We extend the algorithm such that it also finds a flow equal to the min-cut in each phase. The additional time required to find the flow is O.m/ in each phase.
Databáze: OpenAIRE
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