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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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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
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e-ISSN
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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
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