Abstract
To solve reachability is to determine whether there is a path from one vertex to the other in a graph. Standard graph traversal algorithms such as DFS and BFS take linear time to solve reachability; however, their space complexity is also linear. On the other hand, Savitch's algorithm takes quasipolynomial time, although the space-bound is O(log2n). In this paper, we study space-efficient algorithms for deciding reachability that runs in polynomial time.We show a polynomial-time algorithm that solves reachability in directed graphs using O(wlogn) space. Our algorithm requires access to a tree decomposition of width w for the underlying undirected graph of the input. This requirement can be waived for graphs for which recursive balanced vertex separators can be computed space-efficiently.
Published Version
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