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 -