# STCON in directed unique-path graphs

Conference Paper

We study the problem of space-efficient polynomial-time algorithms for directed st-connectivity (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 Õ(nε) space for any constant ε ∈ (0, 1]. We also give a polynomial-time, Õ(n ε)-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 directed cycles. Our results may be viewed along the continuum of sublinear-space polynomial-time algorithms for STCON in different classes of directed graphs - from slightly sublinear-space algorithms for general graphs to O(logn) space algorithms for trees. © S. Kannan, S. Khanna, S. Roy.

### Duke Authors

### Cited Authors

- Kannan, S; Khanna, S; Roy, S

### Published Date

- December 1, 2008

### Published In

### Volume / Issue

- 2 /

### Start / End Page

- 256 - 267

### International Standard Serial Number (ISSN)

- 1868-8969

### International Standard Book Number 13 (ISBN-13)

- 9783939897088

### Citation Source

- Scopus