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1985•SIAM Journal on ComputingRequires access

Maximum Weight Clique Algorithms for Circular-Arc Graphs and Circle Graphs

Wen−Lian Hsu

Open publisher page 66 citations

Abstract

Circle graphs and circular-arc graphs are the intersection graphs of chords and arcs in a circle. In this paper we present algorithms for finding maximum weight cliques in these graphs. The running times of the algorithms are $O(n^2 + m\log \log n)$ for circle graphs and $O(mn)$ for circular-arc graphs. Our algorithms are based on the scanning of appropriate endpoint sequences and efficient bookkeeping of results for subproblems.

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What this paper is about

Circle graphs and circular-arc graphs are the intersection graphs of chords and arcs in a circle. In this paper we present algorithms for finding maximum weight cliques in these graphs. The running times of the algorithms are $O(n^2 + m\log \log n)$ for circle graphs and $O(mn)$ for circular-arc graphs. Our algorithms are based on the scanning of appropriate endpoint sequences and efficient bookkeeping of results for subproblems.

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Available abstract

Circle graphs and circular-arc graphs are the intersection graphs of chords and arcs in a circle. In this paper we present algorithms for finding maximum weight cliques in these graphs. The running times of the algorithms are $O(n^2 + m\log \log n)$ for circle graphs and $O(mn)$ for circular-arc graphs. Our algorithms are based on the scanning of appropriate endpoint sequences and efficient bookkeeping of results for subproblems.

Key concepts: Clique-sum, Chordal graph, Combinatorics, Trapezoid graph, Indifference graph, Mathematics, Circle graph, Arc (geometry)

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