The isomorphism problem for k-trees is complete for logspace
We show that, for k constant, k -tree isomorphism can be decided in logarithmic space by giving an O ( k log n ) 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 Lindell?s 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.
k-trees graph isomorphism graph canonization space complexity logspace completeness