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Polynomial-time algorithm for Maximum Weight Independent Set on P6-free graphs

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Polynomial-time algorithm for Maximum Weight Independent Set on P6-free graphs

  • Original language description

    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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

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

Result continuities

  • Project

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

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

Others

  • Publication year

    2019

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

    978-1-61197-548-2

  • ISSN

  • e-ISSN

  • Number of pages

    15

  • Pages from-to

    1257-1271

  • Publisher name

    SIAM

  • Place of publication

    Neuveden

  • Event location

    San Diego, California, USA

  • Event date

    Jan 6, 2019

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article