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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Shrnutí: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 ].
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-022-10076-x