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.STACS.2016.7
URN: urn:nbn:de:0030-drops-57084
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5708/
Agrawal, Akanksha ;
Lokshtanov, Daniel ;
Mouawad, Amer E. ;
Saurabh, Saket
Simultaneous Feedback Vertex Set: A Parameterized Perspective
Abstract
For a family of graphs F, a graph G, and a positive integer k, the F-DELETION problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-DELETION generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A graph G = (V, cup_{i=1}^{alpha} E_{i}), where the edge set of G is partitioned into alpha color classes, is called an alpha-edge-colored graph. A natural extension of the F-DELETION problem to edge-colored graphs is the alpha-SIMULTANEOUS F-DELETION problem. In the latter problem, we are given an alpha-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph G_i\S, where G_i = (V, E_i) and 1 <= i <= alpha, is in F. In this work, we study alpha-SIMULTANEOUS F-DELETION for F being the family of forests. In other words, we focus on the alpha-SIMULTANEOUS FEEDBACK VERTEX SET (alpha-SIMFVS) problem. Algorithmically, we show that, like its classical counterpart, alpha-SIMFVS parameterized by k is fixed-parameter tractable (FPT) and admits a polynomial kernel, for any fixed constant alpha. In particular, we give an algorithm running in 2^{O(alpha * k)} * n^{O(1)} time and a kernel with O(alpha * k^{3(alpha + 1)}) vertices. The running time of our algorithm implies that alpha-SIMFVS is FPT even when alpha in o(log(n)). We complement this positive result by showing that for alpha in O(log(n)), where n is the number of vertices in the input graph, alpha-SIMFVS becomes W[1]-hard. Our positive results answer one of the open problems posed by Cai and Ye (MFCS 2014).
BibTeX - Entry
@InProceedings{agrawal_et_al:LIPIcs:2016:5708,
author = {Akanksha Agrawal and Daniel Lokshtanov and Amer E. Mouawad and Saket Saurabh},
title = {{Simultaneous Feedback Vertex Set: A Parameterized Perspective}},
booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
pages = {7:1--7:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-001-9},
ISSN = {1868-8969},
year = {2016},
volume = {47},
editor = {Nicolas Ollinger and Heribert Vollmer},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/5708},
URN = {urn:nbn:de:0030-drops-57084},
doi = {10.4230/LIPIcs.STACS.2016.7},
annote = {Keywords: parameterized complexity ,feedback vertex set, kernel, edge-colored graphs}
}
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Keywords: |
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parameterized complexity ,feedback vertex set, kernel, edge-colored graphs |
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Collection: |
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33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016) |
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Issue Date: |
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2016 |
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Date of publication: |
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16.02.2016 |
