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 - 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 - https://www.scopus.com/pages/publications/85069192259
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 -