Surface Split Decompositions and Subgraph Isomorphism in Graphs on Surfaces
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After a sequence of improvements, the current best algorithm for planar graphs is a linear time algorithm by Dorn (STACS '10), with complexity 2^{O(k)} O(n).
We generalize this result, by giving an algorithm of the same complexity for graphs that can be embedded in surfaces of bounded genus. In addition, we simplify the algorithm and analysis. The key to these improvements is the introduction of surface split decompositions for bounded genus graphs, which generalize sphere cut decompositions for planar graphs. We extend the algorithm for the problem of counting and generating all subgraphs isomorphic to P, even for the case where P is disconnected. This answers an open question by Eppstein (JGAA '99).
Analysis of algorithms
parameterized algorithms
graphs on surfaces
subgraph isomorphism
dynamic programming
branch decompositions
counting probl
531-542
Regular Paper
Paul
Bonsma
Paul Bonsma
10.4230/LIPIcs.STACS.2012.531
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
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