TL;DR
This paper introduces the matching interdiction problem, demonstrating its computational complexity and providing a pseudo-polynomial algorithm for graphs with bounded treewidth, advancing understanding of interdiction in graph matchings.
Contribution
The paper formally defines the matching interdiction problem, proves its NP-completeness in simple bipartite graphs, and develops a pseudo-polynomial algorithm for graphs with bounded treewidth.
Findings
Matching interdiction is strongly NP-complete in simple bipartite graphs.
A pseudo-polynomial algorithm is developed for graphs with bounded treewidth.
The approach extends algorithms for bounded treewidth graphs to interdiction problems.
Abstract
In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching in the remaining graph is minimized. In this work we introduce the matching interdiction problem and show that it is strongly NP-complete even when the input is restricted to simple, bipartite graphs with unit edge weights and unit interdiction costs. Furthermore, we present a pseudo-polynomial algorithm for solving the matching interdiction problem on graphs with bounded treewidth. The proposed algorithm extends the approach that is typically used for the creation of efficient algorithms on graphs with bounded treewidth to interdiction problems.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Markov Chains and Monte Carlo Methods