 A deterministic approximation algorithm for the Densest k-Subgraph ProblemFrederic Roupin and Alain Billionnet International Journal of Operational Research, 2008, vol. 3, issue 3, 301-314 Abstract: In the Densest k-Subgraph Problem (DSP), we are given an undirected weighted graph G = (V, E) with n vertices (v1,..., vn). We seek to find a subset of k vertices (k belonging to {1,..., n}) which maximises the number of edges which have their two endpoints in the subset. This problem is NP-hard even for bipartite graphs, and no polynomial-time algorithm with a constant performance guarantee is known for the general case. Several authors have proposed randomised approximation algorithms for particular cases (especially when k = n/c, c>1). But derandomisation techniques are not easy to apply here because of the cardinality constraint, and can have a high computational cost. In this paper, we present a deterministic max(d, 8/9c)-approximation algorithm for the DSP (where d is the density of G). The complexity of our algorithm is only that of linear programming. This result is obtained by using particular optimal solutions of a linear programme associated with the classical 0–1 quadratic formulation of DSP. Keywords: approximation algorithms; complexity; linear programming; quadratic programming; densest k-subgraph problem. (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ids:ijores:v:3:y:2008:i:3:p:301-314 Access Statistics for this article More articles in International Journal of Operational Research from Inderscience Enterprises Ltd |
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