Detail publikačního výsledku

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

ŠEDA, M.

Originální název

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

Anglický název

The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation

Druh

Článek WoS

Originální abstrakt

The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.

Anglický abstrakt

The maximum clique problem is a problem that takes many forms in optimization and related graph theory problems, and also has many applications. Because of its NP-completeness (nondeterministic polynomial time), the question arises of its solvability for larger instances. Instead of the traditional approaches based on the use of approximate or stochastic heuristic methods, we focus here on the use of integer programming models in the GAMS (General Algebraic Modelling System) environment, which is based on exact methods and sophisticated deterministic heuristics incorporated in it. We propose modifications of integer models, derive their time complexities and show their direct use in GAMS. GAMS makes it possible to find optimal solutions to the maximum clique problem for instances with hundreds of vertices and thousands of edges within minutes at most. For extremely large instances, good approximations of the optimum are given in a reasonable amount of time. A great advantage of this approach over all the mentioned algorithms is that even if GAMS does not find the best known solution within the chosen time limit, it displays its value at the end of the calculation as a reachable bound.

Klíčová slova

clique, independent set;,GAMS, NP-complete problem, integer programming

Klíčová slova v angličtině

clique, independent set;,GAMS, NP-complete problem, integer programming

Autoři

ŠEDA, M.

Rok RIV

2024

Vydáno

26.10.2023

Nakladatel

MDPI

Místo

Basel

ISSN

2073-8994

Periodikum

Symmetry-Basel

Svazek

15

Číslo

11

Stát

Švýcarská konfederace

Strany od

1

Strany do

16

Strany počet

16

URL

https://www.mdpi.com/2073-8994/15/11/1979

Plný text v Digitální knihovně

http://hdl.handle.net/11012/245086

BibTex

@article{BUT185001,
  author="Miloš {Šeda}",
  title="The Maximum Clique Problem and Integer Programming Models, Their Modifications, Complexity and Implementation",
  journal="Symmetry-Basel",
  year="2023",
  volume="15",
  number="11",
  pages="1--16",
  doi="10.3390/sym15111979",
  url="https://www.mdpi.com/2073-8994/15/11/1979"
}

Dokumenty

symmetry-15-01979