Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Dual Labeling: Answering Graph Reachability Queries in Constant Time
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Decomposing DAGs into disjoint chains
DEXA'07 Proceedings of the 18th international conference on Database and Expert Systems Applications
A functional, successor list based version of warshall's algorithm with applications
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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Given a directed graph Gwith nnodes and eedges, to check whether a node vis reachable from another node uthrough a path is often required. Such a problem is fundamental to numerous applications, including geographic navigation, Internet routing, ontology queries based on RDF/OWL, and metabolic network, as well as XML indexing. Among them, some involve huge but sparse graphs and require fast answering of reachability queries. In this paper, we propose a novel method called core labeling to handle reachability queries for massive, sparse graphs. The goal is to optimize both query time and labeling time. Our method consists of two schemes: Core-I and Core-II. For the Core-I labeling scheme, both the time and space requirements are bounded by O(n+ e+ s·b), where sis the number of the start nodes of all non-tree edges (edges that do not appear in the spanning tree of G);andbis the width of a subgraph of G. The size of that subgraph is bounded by O(t), where tis the number of all the non-tree edges. The query time of Core-I is bounded by O(logb). The Core-II labeling scheme has constant query time, but the labeling time is increased to O(n+ e+ s·b·logb).