TY - GEN

T1 - Path contraction faster than 2n

AU - Agrawal, Akanksha

AU - Fomin, Fedor V.

AU - Lokshtanov, Daniel

AU - Saurabh, Saket

AU - Tale, Prafullkumar

N1 - Funding Information:
Funding Akanksha Agrawal: During some part of the work, the author was supported by ERC Consolidator Grant SYSTEMATIC-GRAPH (No. 725978). Saket Saurabh: This work is supported by the European Research Council (ERC) via grant LOPPRE, reference no. 819416.
Funding Information:
Akanksha Agrawal: During some part of the work, the author was supported by ERC Consolidator Grant SYSTEMATIC-GRAPH (No. 725978). Saket Saurabh: This work is supported by the European Research Council (ERC) via grant LOPPRE, reference no. 819416.
Publisher Copyright:
© Akanksha Agrawal, Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh, and Prafullkumar Tale; licensed under Creative Commons License CC-BY

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - 3-disjoint connected subgraphs

KW - Enumerating connected sets

KW - Exact exponential time algorithms

KW - Graph algorithms

KW - Path contraction

UR - http://www.scopus.com/inward/record.url?scp=85069192259&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2019.11

DO - 10.4230/LIPIcs.ICALP.2019.11

M3 - Conference contribution

AN - SCOPUS:85069192259

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

A2 - Baier, Christel

A2 - Chatzigiannakis, Ioannis

A2 - Flocchini, Paola

A2 - Leonardi, Stefano

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019

Y2 - 9 July 2019 through 12 July 2019

ER -