Path contraction faster than 2n

Akanksha Agrawal, Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, Prafullkumar Tale

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

A graph G is contractible to a graph H if there is a set X ⊆ 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 ∈ 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 2n · nO(1). In spite of the deceptive simplicity of the problem, beating the 2n · nO(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 1.99987n · nO(1). We also define a problem called 3-Disjoint Connected Subgraphs, and design an algorithm for it that runs in time 1.88n · nO(1). The above algorithm is used as a sub-routine in our algorithm for Path Contraction.

Original languageEnglish
Title of host publication46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
EditorsChristel Baier, Ioannis Chatzigiannakis, Paola Flocchini, Stefano Leonardi
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771092
DOIs
StatePublished - 1 Jul 2019
Event46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 - Patras, Greece
Duration: 9 Jul 201912 Jul 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume132
ISSN (Print)1868-8969

Conference

Conference46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Country/TerritoryGreece
CityPatras
Period9/07/1912/07/19

Keywords

  • 3-disjoint connected subgraphs
  • Enumerating connected sets
  • Exact exponential time algorithms
  • Graph algorithms
  • Path contraction

ASJC Scopus subject areas

  • Software

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