Exact and superpolynomial approximation algorithms for the densest k-subgraph problem
Bourgeois, Nicolas; Giannakos, Aristotelis; Lucarelli, Giorgio; Milis, Ioannis; Paschos, Vangelis (2017), Exact and superpolynomial approximation algorithms for the densest k-subgraph problem, European Journal of Operational Research, 262, 3, p. 894-903. 10.1016/j.ejor.2017.04.034
Type
Article accepté pour publication ou publiéExternal document link
https://hal.inria.fr/hal-01539561Date
2017Journal name
European Journal of Operational ResearchVolume
262Number
3Publisher
Elsevier
Pages
894-903
Publication identifier
Metadata
Show full item recordAuthor(s)
Bourgeois, NicolasGiannakos, Aristotelis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lucarelli, Giorgio

Milis, Ioannis
Paschos, Vangelis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
The densest k-subgraph problem is a generalization of the maximum clique problem, in which we are given a graph and a positive integer k, and we search among all the subsets of k vertices of the input graph for the subset which induces the maximum number of edges. densest k-subgraph is a well known optimization problem with various applications as, for example, in the design of public encryption schemes, the evaluation of certain financial derivatives, the identification of communities with similar characteristics, etc. In this paper, we first present algorithms for finding exact solutions for densest k-subgraph which improve upon the standard exponential time complexity of an exhaustive enumeration by creating a link between the computation of an optimum for this problem to the computation of other graph-parameters such as dominating set, vertex cover, longest path, etc. An FPT algorithm is also proposed which considers as a parameter the size of the minimum vertex cover. Finally, we present several approximation algorithms which run in moderately exponential or parameterized time, describing trade-offs between complexity and approximability. In contrast with most of the algorithms in the bibliography, our algorithms need only polynomial space.Subjects / Keywords
combinatorial optimization; dense subgraphs; exact and parameterized algorithms; superpolynomial approximation algorithmsRelated items
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Lucarelli, Giorgio; Milis, Ioannis; Giannakos, Aristotelis; Paschos, Vangelis; Bourgeois, Nicolas (2013) Communication / Conférence
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Bourgeois, Nicolas; Giannakos, Aristotelis; Lucarelli, Giorgio; Milis, Ioannis; Paschos, Vangelis; Pottié, Olivier (2012) Article accepté pour publication ou publié
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Pottié, Olivier; Paschos, Vangelis; Milis, Ioannis; Lucarelli, Giorgio; Giannakos, Aristotelis; Bourgeois, Nicolas (2010) Communication / Conférence
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Bourgeois, Nicolas; Lucarelli, Giorgio; Milis, Ioannis; Paschos, Vangelis (2009) Communication / Conférence