Restricted Space Algorithms for Isomorphism on Bounded Treewidth Graphs

The Graph Isomorphism problem restricted to graphs of bounded treewidth or bounded tree distance width are known to be solvable in polynomial time [2],[19]. We give restricted space algorithms for these problems proving the following results: • Isomorphism for bounded tree distance width graphs is in L and thus complete for the class. We also show that for this kind of graphs a canon can be computed within logspace. • For bounded treewidth graphs, when both input graphs are given together with a tree decomposition, the problem of whether there is an isomorphism respecting the decompositions is in L. • For bounded treewidth graphs, when one of the input graphs is given with a tree decomposition the isomorphism problem is in LogCFL. • As a corollary the isomorphism problem for bounded treewidth graphs is in LogCFL. This improves the known TC1 upper bound for the problem given by Grohe and Verbitsky [8]. Topics: Complexity, Algorithms, Graph Isomorphism Problem, Treewidth, LogCFL...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Bireswar Das, Jacobo Torán, Fabian Wagner
• Keywords: Graph Isomorphism Problem, Isomorphism Problem, STACS 2010, Theoretical Computer Science, Tree Distance Width