文章基本信息

标题：Incremental Exact Min-Cut in Poly-logarithmic Amortized Update Time
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作者：Gramoz Goranci ; Monika Henzinger ; Mikkel Thorup 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：57
页码：46:1-46:17
DOI：10.4230/LIPIcs.ESA.2016.46
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 1997]. We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon^2) space Monte-Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time.
关键词：Dynamic Graph Algorithms; Minimum Cut; Edge Connectivity