A polyhedral study of the maximum edge subgraph problem

Authors:
Flavia Bonomo;Javier Marenco;Daniela Saban;NicoláS E. Stier-Moses
Affiliations:
Depto. de Computación, FCEyN, Universidad de Buenos Aires and IMAS-CONICET, Argentina;Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina;Depto. de Computación, FCEyN, Universidad de Buenos Aires, Argentina and Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina;Graduate School of Business, Columbia University, USA
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 9
Cited 0

The Boolean quadric polytope: some characteristics, facets and relatives

Mathematical Programming: Series A and B
Min-cut clustering

Mathematical Programming: Series A and B
Cardinality constrained Boolean quadratic polytope

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
On maximum clique problems in very large graphs

External memory algorithms
Greedily finding a dense subgraph

Journal of Algorithms
The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization

Software—Practice & Experience - Special issue on discrete algorithm engineering
Complexity of finding dense subgraphs

Discrete Applied Mathematics
A polyhedral study of the generalized vertex packing problem

Mathematical Programming: Series A and B
A constant approximation algorithm for the densest k-subgraph problem on chordal graphs

Information Processing Letters

Quantified Score

Hi-index	0.04

Visualization

Abstract

The study of cohesive subgroups is an important aspect of social network analysis. Cohesive subgroups are studied using different relaxations of the notion of clique in a graph. For instance, given a graph and an integer k, the maximum edge subgraph problem consists of finding a k-vertex subset such that the number of edges within the subset is maximum. This work proposes a polyhedral approach for this NP-hard problem. We study the polytope associated to an integer programming formulation of the problem, present several families of facet-inducing valid inequalities, and discuss the separation problem associated to these families. Finally, we implement a branch and cut algorithm for this problem. This computational study illustrates the effectiveness of the classes of inequalities presented in this work.