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Polynomial algorithms for open plane graph and subgraph isomorphisms

Abstract : Graphs are used as models in a variety of situations. In some cases, e.g. to model images or maps, the graphs will be drawn in the plane, and this feature can be used to obtain new algorithmic results. In this work, we introduce a special class of graphs, called open plane graphs, which can be used to represent images or maps for robots: they are planar graphs embedded in the plane, in which certain faces can be removed, are absent or unreachable. We give a normal form for such graphs and prove that one can check in polynomial time if two normalised graphs are isomorphic, or if two open plane graphs are equivalent (their normal forms are isomorphic). Then we consider a new kind of subgraphs, built from subsets of faces and called patterns. We show that searching for a pattern in an open plane graph is tractable if and only if the faces are contiguous, that is, we prove that the problem is NP-complete otherwise.
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Submitted on : Wednesday, September 11, 2013 - 12:16:56 PM
Last modification on : Wednesday, April 27, 2022 - 3:49:33 AM
Long-term archiving on: : Thursday, December 12, 2013 - 10:06:23 AM


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Colin de la Higuera, Jean-Christophe Janodet, Émilie Samuel, Guillaume Damiand, Christine Solnon. Polynomial algorithms for open plane graph and subgraph isomorphisms. Theoretical Computer Science, Elsevier, 2013, 498, pp.76-99. ⟨10.1016/j.tcs.2013.05.026⟩. ⟨hal-00832098⟩



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