Proceedings., 33rd Annual Symposium on Foundations of Computer Science (1992)
Pittsburgh, PA, USA
Oct. 24, 1992 to Oct. 27, 1992
D. Eppstein , Dept. of Inf.&Comput. Sci., California Univ., Irvine, CA, USA
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.
sparsification, dynamic graph algorithms, data structures, minimum spanning forests, best swap, graph connectivity, graph 2-edge-connectivity
D. Eppstein, "Sparsification-a technique for speeding up dynamic graph algorithms," Proceedings., 33rd Annual Symposium on Foundations of Computer Science(FOCS), Pittsburgh, PA, USA, 1992, pp. 60-69.