An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

A cactus is a connected graph that does not contain K 4 − e as a minor. Given a graph G = ( V , E ) and an integer k ≥ 0, Cactus Vertex Deletion (also known as Diamond Hitting Set ) is the problem of deciding whether G has a vertex set of size at most k whose removal leaves a forest of cacti. The pr...

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Vydáno v:	Theory of computing systems Ročník 66; číslo 2; s. 502 - 515
Hlavní autoři:	Aoike, Yuuki, Gima, Tatsuya, Hanaka, Tesshu, Kiyomi, Masashi, Kobayashi, Yasuaki, Kobayashi, Yusuke, Kurita, Kazuhiro, Otachi, Yota
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.04.2022 Springer Nature B.V
Témata:	Algorithms Apexes Cacti Computer Science Deletion Diamonds Parameterization Theory of Computation Vertex sets Fixed-parameter tractable Measure and conquer analysis Cactus vertex deletion Even cycle transversal
ISSN:	1432-4350, 1433-0490
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Abstract	A cactus is a connected graph that does not contain K 4 − e as a minor. Given a graph G = ( V , E ) and an integer k ≥ 0, Cactus Vertex Deletion (also known as Diamond Hitting Set ) is the problem of deciding whether G has a vertex set of size at most k whose removal leaves a forest of cacti. The previously best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016 ], which runs in time 26 k n O (1) , where n is the number of vertices of G . In this paper, we design a deterministic algorithm for Cactus Vertex Deletion , which runs in time 17.64 k n O (1) . As an almost straightforward application of our algorithm, we also give a deterministic 17.64 k n O (1) -time algorithm for Even Cycle Transversal , which improves the previous running time 50 k n O (1) of the known deterministic parameterized algorithm due to Misra et al. [WG 2012 ].
AbstractList	A cactus is a connected graph that does not contain K4 − e as a minor. Given a graph G = (V,E) and an integer k ≥ 0, Cactus Vertex Deletion (also known as Diamond Hitting Set) is the problem of deciding whether G has a vertex set of size at most k whose removal leaves a forest of cacti. The previously best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016], which runs in time 26knO(1), where n is the number of vertices of G. In this paper, we design a deterministic algorithm for Cactus Vertex Deletion, which runs in time 17.64knO(1). As an almost straightforward application of our algorithm, we also give a deterministic 17.64knO(1)-time algorithm for Even Cycle Transversal, which improves the previous running time 50knO(1) of the known deterministic parameterized algorithm due to Misra et al. [WG 2012]. A cactus is a connected graph that does not contain K 4 − e as a minor. Given a graph G = ( V , E ) and an integer k ≥ 0, Cactus Vertex Deletion (also known as Diamond Hitting Set ) is the problem of deciding whether G has a vertex set of size at most k whose removal leaves a forest of cacti. The previously best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016 ], which runs in time 26 k n O (1) , where n is the number of vertices of G . In this paper, we design a deterministic algorithm for Cactus Vertex Deletion , which runs in time 17.64 k n O (1) . As an almost straightforward application of our algorithm, we also give a deterministic 17.64 k n O (1) -time algorithm for Even Cycle Transversal , which improves the previous running time 50 k n O (1) of the known deterministic parameterized algorithm due to Misra et al. [WG 2012 ].
Author	Aoike, Yuuki Otachi, Yota Kobayashi, Yasuaki Kiyomi, Masashi Kobayashi, Yusuke Gima, Tatsuya Hanaka, Tesshu Kurita, Kazuhiro
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Cites_doi	10.1007/978-3-642-16533-7 10.1137/140997889 10.1016/j.dam.2017.10.018 10.1016/j.jcss.2006.02.001 10.1007/s00453-017-0317-1 10.1016/j.orl.2003.10.009 10.1007/s10878-013-9691-z 10.1145/1552285.1552286 10.1016/j.tcs.2010.06.026 10.1145/2629620 10.1137/S0097539792228228 10.1007/978-3-642-13036-6_15 10.1007/978-3-662-53536-3_20 10.1109/FOCS.2011.23 10.4230/LIPIcs.ISAAC.2020.34 10.4230/LIPIcs.IPEC.2019.22 10.1007/978-3-319-42634-1_7 10.1137/1.9781611975994.58 10.1007/978-3-642-34611-8_19
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Snippet	A cactus is a connected graph that does not contain K 4 − e as a minor. Given a graph G = ( V , E ) and an integer k ≥ 0, Cactus Vertex Deletion (also known as... A cactus is a connected graph that does not contain K4 − e as a minor. Given a graph G = (V,E) and an integer k ≥ 0, Cactus Vertex Deletion (also known as...
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SubjectTerms	Algorithms Apexes Cacti Computer Science Deletion Diamonds Parameterization Theory of Computation Vertex sets
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Title	An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion
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