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.2020.101
URN: urn:nbn:de:0030-drops-125082
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12508/
Wahlström, Magnus
On Quasipolynomial Multicut-Mimicking Networks and Kernelization of Multiway Cut Problems
Abstract
We show the existence of an exact mimicking network of k^O(log k) edges for minimum multicuts over a set of terminals in an undirected graph, where k is the total capacity of the terminals. Furthermore, if Small Set Expansion has an approximation algorithm with a ratio slightly better than Θ(log n), then a mimicking network of quasipolynomial size can be computed in polynomial time. As a consequence of the latter, several problems would have quasipolynomial kernels, including Edge Multiway Cut, Group Feedback Edge Set for an arbitrary group, 0-Extension for integer-weighted metrics, and Edge Multicut parameterized by the solution and the number of cut requests. The result works via a combination of the matroid-based irrelevant edge approach used in the kernel for s-Multiway Cut with a recursive decomposition and sparsification of the graph along sparse cuts. The main technical contribution is a matroid-based marking procedure that we can show will mark all non-irrelevant edges, assuming that the graph is sufficiently densely connected. The only part of the result that is not currently constructive and polynomial-time computable is the detection of such sparse cuts.
This is the first progress on the kernelization of Multiway Cut problems since the kernel for s-Multiway Cut for constant value of s (Kratsch and Wahlström, FOCS 2012).
BibTeX - Entry
@InProceedings{wahlstrm:LIPIcs:2020:12508,
author = {Magnus Wahlstr{\"o}m},
title = {{On Quasipolynomial Multicut-Mimicking Networks and Kernelization of Multiway Cut Problems}},
booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
pages = {101:1--101:14},
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/2020/12508},
URN = {urn:nbn:de:0030-drops-125082},
doi = {10.4230/LIPIcs.ICALP.2020.101},
annote = {Keywords: Multiway Cut, Kernelization, Small Set Expansion, Mimicking Networks}
}
Keywords: |
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Multiway Cut, Kernelization, Small Set Expansion, Mimicking Networks |
Collection: |
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47th International Colloquium on Automata, Languages, and Programming (ICALP 2020) |
Issue Date: |
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2020 |
Date of publication: |
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29.06.2020 |