A fully dynamic algorithm for maintaining the transitive closure

Authors:
Valerie King;Garry Sagert
Affiliations:
Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada;Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada
Venue:
Journal of Computer and System Sciences - STOC 1999
Year:
2002

Citing 14
Cited 8

Amortized efficiency of a path retrieval data structure

Theoretical Computer Science
Finding paths and deleting edges in directed acyclic graphs

Information Processing Letters
Maintenance of transitive closures and transitive reductions of graphs

Proceedings of the International Workshop WG '87 on Graph-theoretic concepts in computer science
Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
Introduction to algorithms

Introduction to algorithms
The design and analysis of algorithms

The design and analysis of algorithms
Complexity models for incremental computation

Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Size-estimation framework with applications to transitive closure and reachability

Journal of Computer and System Sciences
Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Sampling to provide or to bound: with applications to fully dynamic graph algorithms

Proceedings of the workshop on Randomized algorithms and computation
Fast rectangular matrix multiplication and applications

Journal of Complexity
On certificates and lookahead in dynamic graph problems

Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
An On-Line Edge-Deletion Problem

Journal of the ACM (JACM)
Fully dynamic biconnectivity and transitive closure

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science

Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier

Journal of the ACM (JACM)
A Game Theoretic Approach to the Analysis of Dynamic Networks

Electronic Notes in Theoretical Computer Science (ENTCS)
Maintaining dynamic minimum spanning trees: An experimental study

Discrete Applied Mathematics
Towards polynomial lower bounds for dynamic problems

Proceedings of the forty-second ACM symposium on Theory of computing
Dynamic graph algorithms

Algorithms and theory of computation handbook
GRAIL: scalable reachability index for large graphs

Proceedings of the VLDB Endowment
Dynamic Connectivity: Connecting to Networks and Geometry

SIAM Journal on Computing
Simple deterministic algorithms for fully dynamic maximal matching

Proceedings of the forty-fifth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents an efficient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph; hence, each reachability query of the form "Is there a directed path from i to j?" can be answered in O(1) time. The algorithm is randomized and has a one-sided error; it is correct when answering yes, but has O(1/nc) probability of error when answering no, for any constant c. In acyclic graphs, worst case update time is O(n2). In general graphs, the update time is O(n2.26). The space complexity of the algorithm is O(n2).