Exact MIP-based approaches for finding maximum quasi-cliques and dense subgraphs

Alexander Veremyev (), Oleg A. Prokopyev (), Sergiy Butenko () and Eduardo L. Pasiliao ()
Additional contact information
Alexander Veremyev: University of Florida
Oleg A. Prokopyev: University of Pittsburgh
Sergiy Butenko: Texas A&M University
Eduardo L. Pasiliao: Munitions Directorate, Air Force Research Laboratory

Computational Optimization and Applications, 2016, vol. 64, issue 1, No 7, 177-214

Abstract: Abstract Given a simple graph and a constant $$\gamma \in (0,1]$$ γ ∈ ( 0 , 1 ] , a $$\gamma $$ γ -quasi-clique is defined as a subset of vertices that induces a subgraph with an edge density of at least $$\gamma $$ γ . This well-known clique relaxation model arises in a variety of application domains. The maximum $$\gamma $$ γ -quasi-clique problem is to find a $$\gamma $$ γ -quasi-clique of maximum cardinality in the graph and is known to be NP-hard. This paper proposes new mixed integer programming (MIP) formulations for solving the maximum $$\gamma $$ γ -quasi-clique problem. The corresponding linear programming (LP) relaxations are analyzed and shown to be tighter than the LP relaxations of the MIP models available in the literature on sparse graphs. The developed methodology is naturally generalized for solving the maximum $$f(\cdot )$$ f ( · ) -dense subgraph problem, which, for a given function $$f(\cdot )$$ f ( · ) , seeks for the largest k such that there is a subgraph induced by k vertices with at least f(k) edges. The performance of the proposed exact approaches is illustrated on real-life network instances with up to 10,000 vertices.

Keywords: Quasi-clique; s-Defective clique; Average s-plex; Dense subgraph; Clique relaxation; Mixed integer programming (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-015-9804-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9804-y

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-015-9804-y

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().