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An Efficient Algorithm for Answering Graph Reachability Queries

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2 Author(s)
Yangjun Chen ; Dept. Applied Computer Science, University of Winnipeg, 515 Portage Ave., Winnipeg, Manitoba, Canada R3B 2E9. y.chen@uwinnipeg.ca ; Yibin Chen

Given a directed graph G, to check whether a node v is reachable from another node u through a path is often required. In a database system, such an operation is called a recursion computation or reachability checking and not efficiently supported. The reason for this is that the space to store the whole transitive closure of G is prohibitively high. In this paper, we address this issue and propose an 0(n2 + bnradic(b)) time algorithm to decompose a directed acyclic graph (DAG) into a minimized set of disjoint chains to facilitate reachability checking, where n is the number of the nodes and b is the DAG's width, defined to be the size of a largest node subset U of the DAG such that for every pair of nodes u, v isin U, there does not exist a path from u to v or from v to u. Using this algorithm, we are able to label a graph in 0(be) time and store all the labels in O(bn) space with O(logb) reachability checking time, where e is the number of the edges of the DAG. The method can also be extended to handle cyclic directed graphs. Experiments have been performed, showing that our method is promising.

Published in:

2008 IEEE 24th International Conference on Data Engineering

Date of Conference:

7-12 April 2008