Approximating minimum cuts under insertions
LNCS
Henzinger, Monika H
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/ε 2) for a (2+ε)-approximation, O((log λ)((log n)/ε)2) for a (1+ε)-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 ε>0. The (2+ε)-approximation algorithm and the exact algorithm are deterministic, the (1+ε)-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(n 2 min(√n,κ)). This is a factor of κ faster than the best algorithm for computing the exact size, which takes time O(κ 2 n 2 +κ 3 n 1.5). We give an insertionsonly algorithm for maintaining a (2+ε)-approximation of the minimum vertex cut with amortized insertion time O(n(logκk)/ε).
Springer Nature
1995
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doc-type:conferenceObject
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http://purl.org/coar/resource_type/c_5794
https://research-explorer.ista.ac.at/record/11806
Henzinger MH. Approximating minimum cuts under insertions. In: <i>22nd International Colloquium on Automata, Languages and Programming</i>. Vol 944. Springer Nature; 1995:280–291. doi:<a href="https://doi.org/10.1007/3-540-60084-1_81">10.1007/3-540-60084-1_81</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/3-540-60084-1_81
info:eu-repo/semantics/altIdentifier/issn/0302-9743
info:eu-repo/semantics/altIdentifier/issn/1611-3349
info:eu-repo/semantics/altIdentifier/isbn/9783540494256
info:eu-repo/semantics/closedAccess