Space-Efficient Algorithms for Reachability in Surface-Embedded Graphs

We consider the reachability problem for a certain class of directed acyclic graphs embedded on surfaces. Let G(m, g) be the class of directed acyclic graphs with m = m(n) source vertices embedded on a surface (orientable or non-orientable) of genus g = g(n). We give a log-space reduction that on input G, u, v where G G(m, g) and u and v are two vertices of G, outputs G , u , v where G is directed graph, and u , v are vertices of G , so that (a) there is a directed path from u to v in G if and only if there is a directed path from u to v in G and (b) G has O(m + g) vertices. By a direct application of Savitch's theorem on the reduced instance we get a deterministic O(log n + log2 (m + g))-space algorithm for the reachability problem for graphs in G(m, g). By setting m and g to be 2O( log n) we get that the reachability problem for directed acyclic graphs with 2O( log n) sources embedded on surfaces of genus 2O( log n) is in L (deterministic logarithmic space). Earlier, in thi...

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Derrick Stolee, N. V. Vinodchandran
• Keywords: Acyclic Graphs, ECCC 2010, Hardware, Reachability, Reachability Problem