Space-efficient algorithms for reachability in surface-embedded graphs

Authors

Derrick Stolee, University of Nebraska–LincolnFollow
N. V. Vinodchandran, University of Nebraska-LincolnFollow

Date of this Version

2012

Citation

2012 IEEE 27th Conference on Computational Complexity

Comments

Copyright 2011 IEEE

Abstract

This work presents a log-space reduction which compresses an n-vertex directed acyclic graph with m(n) sources embedded on a surface of genus g(n), to a graph with O(m(n) + g(n)) vertices while preserving reachability between a given pair of vertices. Applying existing algorithms to this reduced graph yields new deterministic algorithms with improved space bounds as well as improved simultaneous time space bounds for the reachability problem over a large class of directed acyclic graphs. Specifically, it significantly extends the class of surface-embedded graphs with log-space reachability algorithms: from planar graphs with O(log n) sources, to graphs with 2^O( √ ^{log n}) sources embedded on a surface of genus 2^O( √ ^{log n}). Additionally, it yields an O(n^1-E) space algorithm with polynomial running time for reachability over graphs with O(n^1-E) sources embedded on surfaces of genus O(n^1-E).