Author:
Yangjun Chen
Affiliation:
University of Winnipeg, Canada
Keyword(s):
Graphs, DAGs, Chains, Paths, Transitive Closure, Reachability Queries.
Related
Ontology
Subjects/Areas/Topics:
Databases and Information Systems Integration
;
Enterprise Information Systems
;
Object-Oriented Database Systems
Abstract:
The problem of decomposing a DAG (directed acyclic graph) into a set of disjoint chains has many applications in data engineering. One of them is the compression of transi¬tive closures to support reachability queries on whether a given node v in a directed graph G is reachable from another node u through a path in G. Recently, an interesting algorithm is proposed by Chen et al. (Y. Chen and Y. Chen, 2008) which claims to be able to decompose G into a minimal set of dis¬joint chains in O(n2 + bn ) time, where n is the number of the nodes of G, and b is 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. However, in some cases, it fails to do so. In this paper, we analyze this algorithm and show the problem. More importantly, a new algorithm is discussed, which can always find a minimal set of disjoint chains in the same time complexity as Chen’s.