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Improved Sparsification (1993) [28 citations — 4 self]

by David Eppstein ,  Zvi Galil ,  Giuseppe F. Italiano
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Abstract:

In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using our improved sparsification technique, we keep track of the following properties: minimum spanning forest, best swap, connectivity, 2-edge-connectivity, and bipartiteness, in time O(n 1/2 ) per edge insertion or deletion; 2-vertex-connectivity and 3-vertex-connectivity, in time O(n) per update; and 4-vertexconnectivity, in time O(n#(n)) per update. # Department of Information and Computer Science, University of California, Irvine, CA 92717. Work supported in part by NSF grant CCR-9258355. + Department of Computer Science, Columbia University, New York, NY 10027 and Department of Computer Science, Tel-Aviv University, Tel-Aviv, Israel. Work supported in part by NSF Grants CCR-901460...

Citations

689 Depth-first search and linear graph algorithms – Tarjan - 1972
131 Dividing a Graph into Triconnected Components – Hopcroft, Tarjan - 1973
130 Data structures for on-line updating of minimum spanning trees – Frederickson - 1983
104 Sparsification—a technique for speeding up dynamic graph algorithms – Eppstein, Galil, et al. - 1997
70 Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees – Frederickson - 1991
50 Balanced matroids – Feder, Mihail - 1992
23 Separator Based Sparsification for Dynamic Planar Graph Algorithms – Eppstein, Galil, et al. - 1993
21 On-line maintenance of the fourconnected components of a graph – Kanevsky, Tamassia, et al. - 1991
16 Fully dynamic biconnectivity in graphs – Rauch - 1995
15 Finding the k smallest spanning trees – Eppstein - 1990
9 Dynamic algorithms for half-space reporting, proximity problems, and geometric minimum spanning trees – Agarwal, Eppstein, et al. - 1992
5 Srinivas, “Algorithms and data structures for an expanded family of matroid intersection problems – Frederickson, A - 1989
1 Tree-weighted neighbors and geometric k smallest spanning trees – Eppstein