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A dynamic programming algorithm for the maximum induced matching problem in permutation graphs

Published: 06 December 2018 Publication History

Abstract

For a finite undirected graph G = (V, E) and a positive integer k ≥ 1, an edge set M ⊆ E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been studied under the name maximum induced matching (MIM for short), i.e., a maximum matching which forms an induced subgraph in G. MIM arises in many applications, such as artificial intelligence, game theory, computer networks, VLSI design and marriage problems. In this paper, we design an O(n2) solution for finding MIM in permutation graphs based on a dynamic programming method on edges with the aid of the sweep line technique. Our result is better than the best known algorithm.

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    cover image ACM Other conferences
    SoICT '18: Proceedings of the 9th International Symposium on Information and Communication Technology
    December 2018
    496 pages
    ISBN:9781450365390
    DOI:10.1145/3287921
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    • SOICT: School of Information and Communication Technology - HUST
    • NAFOSTED: The National Foundation for Science and Technology Development

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    Published: 06 December 2018

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    Author Tags

    1. graph algorithm
    2. maximum induced matching
    3. permutation graph

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