Circle Graph Isomorphism in Almost Linear Time
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Circle graphs are intersection graphs of chords of a circle. In this paper, we present a new algorithm for the circle graph isomorphism problem running in time O((n+m)α(n+m)) where n is the number of vertices, m is the number of edges and α is the inverse Ackermann function. Our algorithm is based on the minimal split decomposition [Cunnigham, 1982] and uses the state-of-art circle graph recognition algorithm [Gioan, Paul, Tedder, Corneil, 2014] in the same running time. It improves the running time O(nm) of the previous algorithm [Hsu, 1995] based on a similar approach.
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