TY - JOUR

T1 - An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

AU - Aoike, Yuuki

AU - Gima, Tatsuya

AU - Hanaka, Tesshu

AU - Kiyomi, Masashi

AU - Kobayashi, Yasuaki

AU - Kobayashi, Yusuke

AU - Kurita, Kazuhiro

AU - Otachi, Yota

N1 - Funding Information:
This work is partially supported by JSPS KAKENHI Grant Numbers JP18H04091, JP18H05291, JP18K11168, JP18K11169, JP19K21537, JP20H05793, JP20K11692, and JP20K19742. The authors thank Kunihiro Wasa for fruitful discussions.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/4

Y1 - 2022/4

N2 - 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].

AB - 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].

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U2 - 10.1007/s00224-022-10076-x

DO - 10.1007/s00224-022-10076-x

M3 - Article

AN - SCOPUS:85128673814

SN - 1432-4350

VL - 66

SP - 502

EP - 515

JO - Theory of Computing Systems

JF - Theory of Computing Systems

IS - 2

ER -