Journal of Graph Algorithms and Applications
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A Faster Algorithm for Maximum Induced Matchings on Circle Graphs
Max Ward, Andrew Gozzard, Michael Wise, and Amitava Datta
Vol. 22, no. 2, pp. 389-396, 2018. Concise paper.
Abstract Circle graphs have applications to RNA bioinformatics, computational chemistry, and VLSI design. Additionally, many problems that are intractable on general graphs are efficient for circle graphs. This has driven research into algorithms for circle graphs. One well known graph problem is to find a maximum induced matching. This is NP-Hard, even for bipartite graphs. No algorithm for this problem that works directly on circle graphs has been proposed. However, since circle graphs are included in interval filament graphs, algorithms for this class can be applied to circle graphs. Unfortunately, this entails a large computational cost of $O(|V|^6)$ time. We propose an algorithm that operates directly on circle graphs, and requires only $O(|V|^3)$ time.
Submitted: April 2018.
Reviewed: June 2018.
Revised: June 2018.
Accepted: July 2018.
Final: July 2018.
Published: August 2018.
Communicated by Giuseppe Liotta