Parameterized Extension Complexity of Independent Set and
Related Problems

J 2018

Parameterized Extension Complexity of Independent Set and Related Problems

GAJARSKÝ, Jakub, Petr HLINĚNÝ a Hans Raj TIWARY

Základní údaje

Originální název

Parameterized Extension Complexity of Independent Set and Related Problems

Autoři

GAJARSKÝ, Jakub (703 Slovensko, domácí), Petr HLINĚNÝ (203 Česká republika, garant, domácí) a Hans Raj TIWARY (356 Indie)

Vydání

Discrete Applied Mathematics, Elsevier Science, 2018, 0166-218X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10201 Computer sciences, information science, bioinformatics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.983

Kód RIV

RIV/00216224:14330/18:00100733

Organizační jednotka

Fakulta informatiky

DOI

http://dx.doi.org/10.1016/j.dam.2017.04.042

UT WoS

000447109400007

Klíčová slova anglicky

parameterized complexity; extension complexity; independent set; FO model checking

Štítky

formela-journal

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 16. 4. 2020 09:57, prof. RNDr. Petr Hliněný, Ph.D.

Anotace

V originále

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))<=O(f(k).n)$ where the function f depends only on the 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.

Návaznosti

GA14-03501S, projekt VaV

Název: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

Investor: Grantová agentura ČR, Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

GA17-00837S, projekt VaV

Název: Strukturální vlastnosti, parametrizovaná řešitelnost a těžkost v kombinatorických problémech

Investor: Grantová agentura ČR, Structural properties, parameterized tractability and hardness in combinatorial problems

Citovat

GAJARSKÝ, Jakub, Petr HLINĚNÝ a Hans Raj TIWARY. Parameterized Extension Complexity of Independent Set and Related Problems. Discrete Applied Mathematics. Elsevier Science, 2018, roč. 248, SI, s. 56-67. ISSN 0166-218X. Dostupné z: https://dx.doi.org/10.1016/j.dam.2017.04.042.

@article{1392989,
   author = {Gajarský, Jakub and Hliněný, Petr and Tiwary, Hans Raj},
   article_number = {SI},
   doi = {http://dx.doi.org/10.1016/j.dam.2017.04.042},
   keywords = {parameterized complexity; extension complexity; independent set; FO model checking},
   language = {eng},
   issn = {0166-218X},
   journal = {Discrete Applied Mathematics},
   title = {Parameterized Extension Complexity of Independent Set and Related Problems},
   url = {http://arxiv.org/abs/1511.08841},
   volume = {248},
   year = {2018}
}

TY  - JOUR
ID  - 1392989
AU  - Gajarský, Jakub - Hliněný, Petr - Tiwary, Hans Raj
PY  - 2018
TI  - Parameterized Extension Complexity of Independent Set and Related Problems
JF  - Discrete Applied Mathematics
VL  - 248
IS  - SI
SP  - 56-67
EP  - 56-67
PB  - Elsevier Science
SN  - 0166218X
KW  - parameterized complexity
KW  - extension complexity
KW  - independent set
KW  - FO model checking
UR  - http://arxiv.org/abs/1511.08841
L2  - http://arxiv.org/abs/1511.08841
N2  - 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))<=O(f(k).n)$ where the function f depends only on the 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.
ER  -

GAJARSKÝ, Jakub, Petr HLINĚNÝ a Hans Raj TIWARY. Parameterized Extension Complexity of Independent Set and Related Problems. \textit{Discrete Applied Mathematics}. Elsevier Science, 2018, roč.~248, SI, s.~56-67. ISSN~0166-218X. Dostupné z: https://dx.doi.org/10.1016/j.dam.2017.04.042.

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