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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