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 -