Parameterized Max Min Feedback Vertex Set

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F25%3A00389716" target="_blank" >RIV/68407700:21240/25:00389716 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/23M1605247" target="_blank" >https://doi.org/10.1137/23M1605247</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/23M1605247" target="_blank" >10.1137/23M1605247</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 dynamic programming techniques, we first present an algorithm of time twO(tw)nO(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vcO(vc)nO(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 vco(vc)nO (1) algorithm would refute the Exponential Time Hypothesis. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed a fixed-parameter tractable branching algorithm with complexity 10knO(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34knO(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 dynamic programming techniques, we first present an algorithm of time twO(tw)nO(1), significantly generalizing a recent algorithm of Gaikwad et al. of time vcO(vc)nO(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 vco(vc)nO (1) algorithm would refute the Exponential Time Hypothesis. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed a fixed-parameter tractable branching algorithm with complexity 10knO(1). We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34knO(1).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

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

2025

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Discrete Mathematics

ISSN

0895-4801

e-ISSN

1095-7146

Svazek periodika

39

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

34

Strana od-do

1587-1620

Kód UT WoS článku

001565641100002

EID výsledku v databázi Scopus

2-s2.0-105014200398