Publication detail

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

ŠEDA, M.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

ŠEDA, M.

Released

26. 10. 2023

Publisher

MDPI

Location

Basel

ISBN

2073-8994

Periodical

Symmetry

Year of study

15

Number

11

State

Swiss Confederation

Pages from

1

Pages to

16

Pages count

16

URL

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

Full text in the Digital Library

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",
  year="2023",
  volume="15",
  number="11",
  pages="1--16",
  doi="10.3390/sym15111979",
  issn="2073-8994",
  url="https://www.mdpi.com/2073-8994/15/11/1979"
}