TY - GEN

T1 - Finding, hitting and packing cycles in subexponential time on unit disk graphs

AU - Fomin, Fedor V.

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© Fedor V. Fomin, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, and Meirav Zehavi.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - We give algorithms with running time 2O(√κ log κ)· nO(1) for the following problems. Given an n-vertex unit disk graph G and an integer k, decide whether G contains a path on exactly/at least k vertices, a cycle on exactly κ vertices, a cycle on at least k vertices, a feedback vertex set of size at most k, and a set of κ pairwise vertex-disjoint cycles. For the first three problems, no subexponential time parameterized algorithms were previously known. For the remaining two problems, our algorithms significantly outperform the previously best known parameterized algorithms that run in time 2O(κ0.75 log κ)· nO(1). Our algorithms are based on a new kind of tree decompositions of unit disk graphs where the separators can have size up to kO(1) and there exists a solution that crosses every separator at most O(√κ) times. The running times of our algorithms are optimal up to the log k factor in the exponent, assuming the Exponential Time Hypothesis.

AB - We give algorithms with running time 2O(√κ log κ)· nO(1) for the following problems. Given an n-vertex unit disk graph G and an integer k, decide whether G contains a path on exactly/at least k vertices, a cycle on exactly κ vertices, a cycle on at least k vertices, a feedback vertex set of size at most k, and a set of κ pairwise vertex-disjoint cycles. For the first three problems, no subexponential time parameterized algorithms were previously known. For the remaining two problems, our algorithms significantly outperform the previously best known parameterized algorithms that run in time 2O(κ0.75 log κ)· nO(1). Our algorithms are based on a new kind of tree decompositions of unit disk graphs where the separators can have size up to kO(1) and there exists a solution that crosses every separator at most O(√κ) times. The running times of our algorithms are optimal up to the log k factor in the exponent, assuming the Exponential Time Hypothesis.

KW - Cycle packing

KW - Feedback vertex set

KW - Longest cycle

KW - Parameterized complexity

KW - Unit disk graph

UR - http://www.scopus.com/inward/record.url?scp=85027256676&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2017.65

DO - 10.4230/LIPIcs.ICALP.2017.65

M3 - Conference contribution

AN - SCOPUS:85027256676

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017

A2 - Muscholl, Anca

A2 - Indyk, Piotr

A2 - Kuhn, Fabian

A2 - Chatzigiannakis, Ioannis

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

T2 - 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017

Y2 - 10 July 2017 through 14 July 2017

ER -