Improved Sparsification (1993) [28 citations — 4 self]
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author = {David Eppstein and Zvi Galil and Giuseppe F. Italiano},
title = {Improved Sparsification},
institution = {},
year = {1993}
}
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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...
