Log-space Algorithms for Paths and Matchings in k-trees

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [14]. However, for graphs of treewidth larger than 2, no bound better than NL is known. In this paper, we improve these bounds for k-trees, where k is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed k-trees, and for computation of shortest and longest paths in directed acyclic k-trees. Besides the path problems mentioned above, we consider the problem of deciding whether a k-tree has a perfect macthing (decision version), and if so, finding a perfect matching (search version), and prove that these problems are L-complete. These problems are known to be in P and in RNC for general graphs, and in SPL for planar bipartite graphs [8]. Our results settle the complexity of these problems for the class of k-trees. The results are also applicable for bounded tree-width graphs, when a tree-decomposition i...

• Type: Conference
• Year: 2010
• Where: STACS
• Authors: Bireswar Das, Samir Datta, Prajakta Nimbhorkar
• Keywords: General Graphs, Path Problems, Shortest Path Problems, STACS 2010, Theoretical Computer Science