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.IPEC.2015.78
URN: urn:nbn:de:0030-drops-55738
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5573/
Kim, Eun Jung ;
Paul, Christophe ;
Sau, Ignasi ;
Thilikos, Dimitrios M.
Parameterized Algorithms for Min-Max Multiway Cut and List Digraph Homomorphism
Abstract
In this paper we design FPT-algorithms for two parameterized problems. The first is List Digraph Homomorphism: given two digraphs G and H and a list of allowed vertices of H for every vertex of G, the question is whether there exists a homomorphism from G to H respecting the list constraints. The second problem is a variant of Multiway Cut, namely Min-Max Multiway Cut: given a graph G, a non-negative integer l, and a set T of r terminals, the question is whether we can partition the vertices of G into r parts such that (a) each part contains one terminal and (b) there are at most l edges with only one endpoint in this part. We parameterize List Digraph Homomorphism by the number w of edges of G that are mapped to non-loop edges of H and we give a time 2^{O(l * log(h) + l^{2 * log(l)}} * n^{4} * log(n) algorithm, where h is the order of the host graph H.We also prove that Min-Max Multiway Cut can be solved in time 2^{O((l * r)^2 * log(l *r))} * n^{4} * log(n). Our approach introduces a general problem, called List Allocation, whose expressive power permits the design of parameterized reductions of both aforementioned problems to it. Then our results are based on an FPT-algorithm for the List Allocation problem that is designed using a suitable adaptation of the randomized contractions technique (introduced by [Chitnis, Cygan, Hajiaghayi, Pilipczuk, and Pilipczuk, FOCS 2012]).
BibTeX - Entry
@InProceedings{kim_et_al:LIPIcs:2015:5573,
author = {Eun Jung Kim and Christophe Paul and Ignasi Sau and Dimitrios M. Thilikos},
title = {{Parameterized Algorithms for Min-Max Multiway Cut and List Digraph Homomorphism}},
booktitle = {10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
pages = {78--89},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-92-7},
ISSN = {1868-8969},
year = {2015},
volume = {43},
editor = {Thore Husfeldt and Iyad Kanj},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5573},
URN = {urn:nbn:de:0030-drops-55738},
doi = {10.4230/LIPIcs.IPEC.2015.78},
annote = {Keywords: Parameterized complexity, Fixed-Parameter Tractable algorithm, Multiway Cut, Digraph homomorphism}
}
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Keywords: |
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Parameterized complexity, Fixed-Parameter Tractable algorithm, Multiway Cut, Digraph homomorphism |
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Collection: |
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10th International Symposium on Parameterized and Exact Computation (IPEC 2015) |
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Issue Date: |
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2015 |
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Date of publication: |
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19.11.2015 |
