Parameterized extension complexity of independent set and related problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387251" target="_blank" >RIV/00216208:11320/18:10387251 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14330/18:00100733

Výsledek na webu

<a href="https://doi.org/10.1016/j.dam.2017.04.042" target="_blank" >https://doi.org/10.1016/j.dam.2017.04.042</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2017.04.042" target="_blank" >10.1016/j.dam.2017.04.042</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameterized extension complexity of independent set and related problems

Popis výsledku v původním jazyce

Let G be a graph on n vertices and STAB(k)(G) be the convex hull of characteristic vectors of its independent sets of size at most k. We study extension complexity of STAB(k)(G) with respect to a fixed parameter k (analogously to, e.g., parameterized computational complexity of problems). We show that for graphs G from a class of bounded expansion it holds that xc(STAB(k)(G)) &lt;= O(f(k) . n) where the function f depends only on the class. This result can be extended in a simple way to a wide range of similarly defined graph polytopes. In case of general graphs we show that there is no function f such that, for all values of the parameter k and for all graphs on n vertices, the extension complexity of STAB(k)(G) is at most f (k) . n(O(1)). While such results are not surprising since it is known that optimizing over STAB(k)(G) is FPT for graphs of bounded expansion and W [1]-hard in general, they are also not trivial and in both cases stronger than the corresponding computational complexity results. (C) 2017 Published by Elsevier B.V.

Název v anglickém jazyce

Parameterized extension complexity of independent set and related problems

Popis výsledku anglicky

Let G be a graph on n vertices and STAB(k)(G) be the convex hull of characteristic vectors of its independent sets of size at most k. We study extension complexity of STAB(k)(G) with respect to a fixed parameter k (analogously to, e.g., parameterized computational complexity of problems). We show that for graphs G from a class of bounded expansion it holds that xc(STAB(k)(G)) &lt;= O(f(k) . n) where the function f depends only on the class. This result can be extended in a simple way to a wide range of similarly defined graph polytopes. In case of general graphs we show that there is no function f such that, for all values of the parameter k and for all graphs on n vertices, the extension complexity of STAB(k)(G) is at most f (k) . n(O(1)). While such results are not surprising since it is known that optimizing over STAB(k)(G) is FPT for graphs of bounded expansion and W [1]-hard in general, they are also not trivial and in both cases stronger than the corresponding computational complexity results. (C) 2017 Published by Elsevier B.V.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

—

Svazek periodika

248

Číslo periodika v rámci svazku

October

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

56-67

Kód UT WoS článku

000447109400007

EID výsledku v databázi Scopus

2-s2.0-85019902319