Bandwidth Parameterized by Cluster Vertex Deletion Number

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00370210" target="_blank" >RIV/68407700:21240/23:00370210 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4230/LIPIcs.IPEC.2023.21" target="_blank" >https://doi.org/10.4230/LIPIcs.IPEC.2023.21</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.IPEC.2023.21" target="_blank" >10.4230/LIPIcs.IPEC.2023.21</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bandwidth Parameterized by Cluster Vertex Deletion Number

Popis výsledku v původním jazyce

Given a graph G and an integer b, Bandwidth asks whether there exists a bijection π from V(G) to {1, ..., |V(G)|} such that max_{{u, v} element E(G)} | π(u) - π(v) | <= b. This is a classical NP-complete problem, known to remain NP-complete even on very restricted classes of graphs, such as trees of maximum degree 3 and caterpillars of hair length 3. In the realm of parameterized complexity, these results imply that the problem remains NP-hard on graphs of bounded pathwidth, while it is additionally known to be W[1]-hard when parameterized by the treedepth of the input graph. In contrast, the problem does become FPT when parameterized by the vertex cover number of the input graph. In this paper, we make progress towards the parameterized (in)tractability of Bandwidth. We first show that it is FPT when parameterized by the cluster vertex deletion number cvd plus the clique number ω of the input graph, thus generalizing the previously mentioned result for vertex cover. On the other hand, we show that Bandwidth is W[1]-hard when parameterized only by cvd. Our results generalize some of the previous results and narrow some of the complexity gaps.

Název v anglickém jazyce

Bandwidth Parameterized by Cluster Vertex Deletion Number

Popis výsledku anglicky

Given a graph G and an integer b, Bandwidth asks whether there exists a bijection π from V(G) to {1, ..., |V(G)|} such that max_{{u, v} element E(G)} | π(u) - π(v) | <= b. This is a classical NP-complete problem, known to remain NP-complete even on very restricted classes of graphs, such as trees of maximum degree 3 and caterpillars of hair length 3. In the realm of parameterized complexity, these results imply that the problem remains NP-hard on graphs of bounded pathwidth, while it is additionally known to be W[1]-hard when parameterized by the treedepth of the input graph. In contrast, the problem does become FPT when parameterized by the vertex cover number of the input graph. In this paper, we make progress towards the parameterized (in)tractability of Bandwidth. We first show that it is FPT when parameterized by the cluster vertex deletion number cvd plus the clique number ω of the input graph, thus generalizing the previously mentioned result for vertex cover. On the other hand, we show that Bandwidth is W[1]-hard when parameterized only by cvd. Our results generalize some of the previous results and narrow some of the complexity gaps.

Druh

D - Stať ve sborníku

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

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 18th International Symposium on Parameterized and Exact Computation

ISBN

978-3-95977-305-8

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

15

Strana od-do

"21:1"-"21:15"

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl

Místo konání akce

Amsterdam

Datum konání akce

6. 9. 2023

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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