Author:
Yangjun Chen
Affiliation:
University of Winnipeg, Canada
Keyword(s):
General Spanning Trees, Core Labelling, Reachability Queries, Transitive Closure.
Related
Ontology
Subjects/Areas/Topics:
Algorithms and Data Structures
;
Programming Languages
;
Software Engineering
Abstract:
The checking of graph reachability is an important opera¬tion in many applications, by which for two given nodes u and v in a directed graph G we will check whether u is reachable from v through a path in G or vice versa. In this paper, we focus ourselves on this issue. A new approach is proposed to compress transitive closure to support reach¬ability. The main idea is the concept of general spanning trees, as well as a new labeling technique, called core labeling. For a graph G with n nodes and e edges, the labeling time is bounded by O(n + e + tb), where t is the number of non-tree edges (edges that do not appear in the general spanning tree T of G) and b is the number of the leaf nodes of T. It can be proven that b equals G’s width, defined to be the size of a largest node subset U of G such that for every pair of nodes u, v U, there does not exist a path from u to v or from v to u. The space and time com¬plexities are bounded by O(n + tb) and O(logb), respectively.