Parameterized Max Min Feedback Vertex Set

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00370181" target="_blank" >RIV/68407700:21240/23:00370181 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.MFCS.2023.62" target="_blank" >https://doi.org/10.4230/LIPIcs.MFCS.2023.62</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.MFCS.2023.62" target="_blank" >10.4230/LIPIcs.MFCS.2023.62</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameterized Max Min Feedback Vertex Set

Popis výsledku v původním jazyce

Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).

Název v anglickém jazyce

Parameterized Max Min Feedback Vertex Set

Popis výsledku anglicky

Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw^O(tw) n^O(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vc^O(vc) n^O(1), where tw, vc denote the input graph’s treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc^o(vc) n^O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10^k n^O(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34^k n^O(1).

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 48th International Symposium on Mathematical Foundations of Computer Science

ISBN

978-3-95977-292-1

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

15

Strana od-do

"62:1"-"62:15"

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Bordeaux

Datum konání akce

28. 8. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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