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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.2019.11
URN: urn:nbn:de:0030-drops-105874
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10587/
Agrawal, Akanksha ;
Fomin, Fedor V. ;
Lokshtanov, Daniel ;
Saurabh, Saket ;
Tale, Prafullkumar
Path Contraction Faster Than 2^n
Abstract
A graph G is contractible to a graph H if there is a set X subseteq E(G), such that G/X is isomorphic to H. Here, G/X is the graph obtained from G by contracting all the edges in X. For a family of graphs F, the F-Contraction problem takes as input a graph G on n vertices, and the objective is to output the largest integer t, such that G is contractible to a graph H in F, where |V(H)|=t. When F is the family of paths, then the corresponding F-Contraction problem is called Path Contraction. The problem Path Contraction admits a simple algorithm running in time 2^n * n^{O(1)}. In spite of the deceptive simplicity of the problem, beating the 2^n * n^{O(1)} bound for Path Contraction seems quite challenging. In this paper, we design an exact exponential time algorithm for Path Contraction that runs in time 1.99987^n * n^{O(1)}. We also define a problem called 3-Disjoint Connected Subgraphs, and design an algorithm for it that runs in time 1.88^n * n^{O(1)}. The above algorithm is used as a sub-routine in our algorithm for Path Contraction.
BibTeX - Entry
@InProceedings{agrawal_et_al:LIPIcs:2019:10587,
author = {Akanksha Agrawal and Fedor V. Fomin and Daniel Lokshtanov and Saket Saurabh and Prafullkumar Tale},
title = {{Path Contraction Faster Than 2^n}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {11:1--11:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10587},
URN = {urn:nbn:de:0030-drops-105874},
doi = {10.4230/LIPIcs.ICALP.2019.11},
annote = {Keywords: path contraction, exact exponential time algorithms, graph algorithms, enumerating connected sets, 3-disjoint connected subgraphs}
}
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Keywords: |
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path contraction, exact exponential time algorithms, graph algorithms, enumerating connected sets, 3-disjoint connected subgraphs |
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Collection: |
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46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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04.07.2019 |
