Issue |
RAIRO-Oper. Res.
Volume 55, Number 5, September-October 2021
|
|
---|---|---|
Page(s) | 3121 - 3140 | |
DOI | https://doi.org/10.1051/ro/2021150 | |
Published online | 21 October 2021 |
A matheuristic approach for the maximum balanced subgraph of a signed graph
Computer Science Department, Universidade Federal Fluminense, Niterói, RJ, Brazil
* Corresponding author: jorge85.mail@gmail.com
Received:
25
January
2021
Accepted:
20
September
2021
A graph G = (V, E) with its edges labeled in the set {+,-} is called a signed graph. It is balanced if its set of vertices V can be partitioned into two sets V1 and V2, such that all positive edges connect nodes within V1 or V2, and all negative edges connect nodes between V1 and V2. The maximum balanced subgraph problem (MBSP) for a signed graph is the problem of finding a balanced subgraph with the maximum number of vertices. In this work, we present the first polynomial integer linear programming formulation for this problem and a matheuristic to obtain good quality solutions in a short time. The results obtained for different sets of instances show the effectiveness of the matheuristic, optimally solving several instances and finding better results than the exact method in a much shorter computational time.
Mathematics Subject Classification: 90C59 / 90C27 / 90C05 / 90C10
Key words: Balanced signed graph / local search / matheuristic
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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