Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
426548 | Information and Computation | 2012 | 11 Pages |
We show that, for k constant, k -tree isomorphism can be decided in logarithmic space by giving an O(klogn) space canonical labeling algorithm. The algorithm computes a unique tree decomposition, uses colors to fully encode the structure of the original graph in the decomposition tree and invokes Lindellʼs tree canonization algorithm. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for k-trees are all complete for deterministic logspace. Completeness for logspace holds even for simple structural properties of k -trees. We also show that a variant of our canonical labeling algorithm runs in time O((k+1)!n), where n is the number of vertices, yielding the fastest known FPT algorithm for k-tree isomorphism.