License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2020.65
URN: urn:nbn:de:0030-drops-124725
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12472/
Hirai, Hiroshi ;
Ikeda, Motoki
Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity
Abstract
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)⋅ MF(kn,m+k²n)) 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 Lovász - Cherkassky theorem to the node-capacity setting. Our results build on discrete convex analysis for the node-connectivity terminal backup problem.
BibTeX - Entry
@InProceedings{hirai_et_al:LIPIcs:2020:12472,
author = {Hiroshi Hirai and Motoki Ikeda},
title = {{Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {65:1--65:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-138-2},
ISSN = {1868-8969},
year = {2020},
volume = {168},
editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12472},
URN = {urn:nbn:de:0030-drops-124725},
doi = {10.4230/LIPIcs.ICALP.2020.65},
annote = {Keywords: terminal backup problem, node-connectivity, separately-capacitated multiflow, discrete convex analysis}
}
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Keywords: |
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terminal backup problem, node-connectivity, separately-capacitated multiflow, discrete convex analysis |
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Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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29.06.2020 |
