文章基本信息

标题：Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity
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作者：Hiroshi Hirai ; Motoki Ikeda
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：65:1-65:19
DOI：10.4230/LIPIcs.ICALP.2020.65
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The terminal backup problems [Anshelevich and Karagiozova, 2011] form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to find a minimum cost subgraph satisfying the connectivity requirement. The node-connectivity terminal backup problem requires a terminal to connect other terminals with a number of node-disjoint paths. This problem is not known whether is NP-hard or tractable. Fukunaga (2016) gave a 4/3-approximation algorithm based on LP-rounding scheme using a general LP-solver. In this paper, we develop a combinatorial algorithm for the relaxed LP to find a half-integral optimal solution in O(mlog (mUA)â<. MF(kn,m+kÂ²n)) time, where m is the number of edges, k is the number of terminals, A is the maximum edge-cost, U is the maximum edge-capacity, and MF(n',m') is the time complexity of a max-flow algorithm in a network with n' nodes and m' edges. The algorithm implies that the 4/3-approximation algorithm for the node-connectivity terminal backup problem is also efficiently implemented. For the design of algorithm, we explore a connection between the node-connectivity terminal backup problem and a new type of a multiflow, called a separately-capacitated multiflow. We show a min-max theorem which extends LovÃ¡sz - Cherkassky theorem to the node-capacity setting. Our results build on discrete convex analysis for the node-connectivity terminal backup problem.
关键词：terminal backup problem; node-connectivity; separately-capacitated multiflow; discrete convex analysis