Deciding Circular-Arc Graph Isomorphism in Parameterized Logspace

Author Maurice Chandoo



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Maurice Chandoo

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Maurice Chandoo. Deciding Circular-Arc Graph Isomorphism in Parameterized Logspace. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 26:1-26:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.STACS.2016.26

Abstract

We compute a canonical circular-arc representation for a given circular-arc (CA) graph which implies solving the isomorphism and recognition problem for this class. To accomplish this we split the class of CA graphs into uniform and non-uniform ones and employ a generalized version of the argument given by Köbler et al. (2013) that has been used to show that the subclass of Helly CA graphs can be canonized in logspace. For uniform CA graphs our approach works in logspace and in addition to that Helly CA graphs are a strict subset of uniform CA graphs. Thus our result is a generalization of the canonization result for Helly CA graphs. In the non-uniform case a specific set Omega of ambiguous vertices arises. By choosing the parameter k to be the cardinality of Omega this obstacle can be solved by brute force. This leads to an O(k + log(n)) space algorithm to compute a canonical representation for non-uniform and therefore all CA graphs.
Keywords
  • graph isomorphism
  • canonical representation
  • parameterized algorithm

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References

  1. Andrew Curtis, Min Chih Lin, Ross McConnell, Yahav Nussbaum, Francisco Soulignac, Jeremy Spinrad, and Jayme Szwarcfiter. Isomorphism of graph classes related to the circular-ones property. Discrete Mathematics and Theoretical Computer Science, 15(1), 2013. URL: http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2298.
  2. Elaine Marie Eschen. Circular-arc Graph Recognition and Related Problems. PhD thesis, Vanderbilt University, Nashville, TN, USA, 1998. UMI Order No. GAX98-03921. Google Scholar
  3. Wen-Lian Hsu. O(M ⋅ N) algorithms for the recognition and isomorphism problems on circular-arc graphs. SIAM J. Comput., 24(3):411-439, June 1995. URL: http://dx.doi.org/10.1137/S0097539793260726.
  4. Johannes Köbler, Sebastian Kuhnert, and Oleg Verbitsky. Solving the Canonical Representation and Star System Problems for Proper Circular-Arc Graphs in Logspace. In FSTTCS, volume 18, pages 387-399. Schloss Dagstuhl, 2012. Google Scholar
  5. Johannes Köbler, Sebastian Kuhnert, Bastian Laubner, and Oleg Verbitsky. Interval graphs: Canonical representations in logspace. SIAM J. Comput., 40(5):1292-1315, 2011. URL: http://dx.doi.org/10.1137/10080395X.
  6. Johannes Köbler, Sebastian Kuhnert, and Oleg Verbitsky. Helly circular-arc graph isomorphism is in logspace. In MFCS 2013, volume 8087 of Lecture Notes in Computer Science, pages 631-642. Springer Berlin Heidelberg, 2013. URL: http://dx.doi.org/10.1007/978-3-642-40313-2_56.
  7. George S. Lueker and Kellogg S. Booth. A linear time algorithm for deciding interval graph isomorphism. J. ACM, 26(2):183-195, April 1979. URL: http://dx.doi.org/10.1145/322123.322125.
  8. Ross M. McConnell. Linear-time recognition of circular-arc graphs. Algorithmica, 37(2):93-147, 2003. URL: http://dx.doi.org/10.1007/s00453-003-1032-7.
  9. Tsong-Ho Wu. An O(n³) Isomorphism Test for Circular-Arc Graphs. PhD thesis, SUNY Stony Brook, New York, NY, USA, 1983. Google Scholar
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