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- W1584687374 abstract "This paper presents insertions-only algorithms for maintaining the exact and approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) or O(log n) and a cut of size k in time linear in its size. The amortized time per insertion is O(1/e2) for a (2+e)-approximation, O((log λ)((log n)/e)2) for a (1+e)-approximation, and O(λ log n) for the exact size of the minimum edge cut, where n is the number of nodes in the graph, λ is the size of the minimum cut and e>0. The (2+e)-approximation algorithm and the exact algorithm are deterministic, the (1+e)-approximation algorithm is randomized. The algorithms are optimal in the sense that the time needed for m insertions matches the time needed by the best static algorithm on a m-edge graph. We also present a static 2-approximation algorithm for the size κ of the minimum vertex cut in a graph, which takes time O(n2min(√n,κ)). This is a factor of κ faster than the best algorithm for computing the exact size, which takes time O(κ2n2+κ3n1.5). We give an insertionsonly algorithm for maintaining a (2+e)-approximation of the minimum vertex cut with amortized insertion time O(n(logκk)/e)." @default.
- W1584687374 created "2016-06-24" @default.
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- W1584687374 date "1995-01-01" @default.
- W1584687374 modified "2023-10-07" @default.
- W1584687374 title "Approximating minimum cuts under insertions" @default.
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- W1584687374 doi "https://doi.org/10.1007/3-540-60084-1_81" @default.
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