Deterministic Õ(nm) time edge-splitting in undirected graphs
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Augmenting undirected edge connectivity in Õ(n2) time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Minimum cuts in near-linear time
Journal of the ACM (JACM)
Planarity of the 2-Level Cactus Model
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
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Let G be an undirected c-edge connected graph. In this paper we give an O(n/sup 2/)-sized planar geometric representation for all edge cuts with capacity less than 6/5c. The representation can be very efficiently built, by using a single run of the Karger-Stein algorithm for finding near-mincuts. We demonstrate that the representation provides an efficient query structure for near-mincuts, as well as a new proof technique through geometric arguments. We show that in algorithms based on edge splitting, computing our representation O(log n) times substitute for one, or sometimes even /spl Omega/(n), u-/spl nu/ mincut computations; this can lead to significant savings, since our representation can be computed /spl theta//spl tilde/(m/n) times faster than the currently best known u-/spl nu/ mincut algorithm. We also improve the running time of the edge augmentation problem, provided the initial edge weights are polynomially bounded.