STCON in Directed Unique-Path Graphs

ABSTRACT. We study the problem of space-efficient polynomial-time algorithms for directed stconnectivity (STCON). Given a directed graph G, and a pair of vertices s, t, the STCON problem is to decide if there exists a path from s to t in G. For general graphs, the best polynomial-time algorithm for STCON uses space that is only slightly sublinear. However, for special classes of directed graphs, polynomial-time poly-logarithmic-space algorithms are known for STCON. In this paper, we continue this thread of research and study a class of graphs called unique-path graphs with respect to source s, where there is at most one simple path from s to any vertex in the graph. For these graphs, we give a polynomial-time algorithm that uses ˜O(nε) space for any constant ε ∈ (0, 1]. We also give a polynomial-time, ˜O(nε)-space algorithm to recognize unique-path graphs. Unique-path graphs are related to configuration graphs of unambiguous log-space computations, but they can have some direc...

• Type: Conference
• Year: 2008
• Where: FSTTCS
• Authors: Sampath Kannan, Sanjeev Khanna, Sudeepa Roy
• Keywords: Directed Graphs, FSTTCS 2008, Polynomial-time Algorithm, Software Engineering, Unique-path Graphs