Polynomial-time Algorithm for Maximum Weight Independent Set on P6-free Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455778" target="_blank" >RIV/00216208:11320/22:10455778 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9l0I.d-wh0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=9l0I.d-wh0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3414473" target="_blank" >10.1145/3414473</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial-time Algorithm for Maximum Weight Independent Set on P6-free Graphs

Popis výsledku v původním jazyce

In the classic Maximum Weight Independent Set problem, we are given a graph G with a nonnegative weight function on its vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any P6-free graph, that is, a graph that has no path on 6 vertices as an induced subgraph. This improves the polynomial-time algorithm on P5-free graphs of Lokshtanov et al. [15] and the quasipolynomial-time algorithm on P6-free graphs of Lokshtanov et al. [14]. The main technical contribution leading to our main result is enumeration of a polynomial-size family ℱ of vertex subsets with the following property: For every maximal independent set I in the graph, ℱ contains all maximal cliques of some minimal chordal completion of G that does not add any edge incident to a vertex of I.

Název v anglickém jazyce

Polynomial-time Algorithm for Maximum Weight Independent Set on P6-free Graphs

Popis výsledku anglicky

In the classic Maximum Weight Independent Set problem, we are given a graph G with a nonnegative weight function on its vertices, and the goal is to find an independent set in G of maximum possible weight. While the problem is NP-hard in general, we give a polynomial-time algorithm working on any P6-free graph, that is, a graph that has no path on 6 vertices as an induced subgraph. This improves the polynomial-time algorithm on P5-free graphs of Lokshtanov et al. [15] and the quasipolynomial-time algorithm on P6-free graphs of Lokshtanov et al. [14]. The main technical contribution leading to our main result is enumeration of a polynomial-size family ℱ of vertex subsets with the following property: For every maximal independent set I in the graph, ℱ contains all maximal cliques of some minimal chordal completion of G that does not add any edge incident to a vertex of I.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

ACM Transactions on Algorithms

ISSN

1549-6325

e-ISSN

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Svazek periodika

Neuveden

Číslo periodika v rámci svazku

18

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

57

Strana od-do

1-57

Kód UT WoS článku

000944887800004

EID výsledku v databázi Scopus

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