Sparsification-a technique for speeding up dynamic graph algorithms

Authors:
D. Eppstein
Affiliations:
Dept. of Inf.&Comput. Sci., California Univ., Irvine, CA, USA
Venue:
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Year:
1992

Citing 0
Cited 4

Dynamic Reorganization of Object Databases

IDEAS '99 Proceedings of the 1999 International Symposium on Database Engineering & Applications
Quality of EDA CAD Tools: Definitions, Metrics and Directions

ISQED '00 Proceedings of the 1st International Symposium on Quality of Electronic Design
Basic data structures

Algorithms and theory of computation handbook
Computing with Time-Varying Data: Sequential Complexity and Parallel Speed-Up

Theory of Computing Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

The authors provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties: minimum spanning forests, best swap, graph connectivity, and graph 2-edge-connectivity, in time O(n/sup 1/2/log(m/n)) per change; 3-edge-connectivity, in time O(n/sup 2/3/) per change; 4-edge-connectivity, in time O(n alpha (n)) per change; k-edge-connectivity, in time O(n log n) per change; bipartiteness, 2-vertex-connectivity, and 3-vertex-connectivity, in time O(n log(m/n)) per change; and 4-vertex-connectivity, in time O(n log(m/n)+n alpha (n)) per change. Further results speed up the insertion times to match the bounds of known partially dynamic algorithms. The algorithms are based on a technique that transforms algorithms for sparse graphs into ones that work on any graph, which they call sparsification.