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%2F19%3A10404617" target="_blank" >RIV/00216208:11320/19:10404617 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/1.9781611975482.77" target="_blank" >https://doi.org/10.1137/1.9781611975482.77</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/1.9781611975482.77" target="_blank" >10.1137/1.9781611975482.77</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 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. (SODA 2014), and the quasipolynomial-time algorithm on P6-free graphs of Lokshtanov et al (SODA 2016). 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 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. (SODA 2014), and the quasipolynomial-time algorithm on P6-free graphs of Lokshtanov et al (SODA 2016). 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

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

<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

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

ISBN

978-1-61197-548-2

ISSN

—

e-ISSN

—

Počet stran výsledku

15

Strana od-do

1257-1271

Název nakladatele

SIAM

Místo vydání

Neuveden

Místo konání akce

San Diego, California, USA

Datum konání akce

6. 1. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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