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The Dense kSubgraph Problem
 Algorithmica
, 1999
"... This paper considers the problem of computing the dense kvertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(n ffi ), for some ffi ! 1=3. 1 Introduction We study the dense ksubgraph (D ..."
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Cited by 205 (12 self)
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This paper considers the problem of computing the dense kvertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(n ffi ), for some ffi ! 1=3. 1 Introduction We study the dense ksubgraph
Polynomial integrality gaps for strong SDP relaxations of Densest ksubgraph
"... The Densest ksubgraph problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant gap between known upper and lower bounds for Densest ksubgraph: the current best algorithm gives an ≈ O(n 1/4) approximatio ..."
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Cited by 15 (4 self)
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the approximability of Densest ksubgraph is an important challenge. In this work, we give evidence for the hardness of approximating Densest ksubgraph within polynomial factors. Specifically, we expose the limitations of strong semidefinite programs from SDP hierarchies in solving Densest ksubgraph. Our results
Exact and approximation algorithms for densest ksubgraph
, 2012
"... The densest ksubgraph problem is a generalization of the maximum clique problem, in which we are given a graph G and a positive integer k, and we search among the subsets of k vertices of G one inducing a maximum number of edges. In this paper, we present algorithms for finding exact solutions of d ..."
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Cited by 5 (1 self)
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of densest ksubgraph improving the standard exponential time complexity of O ∗ (2 n) and using polynomial space. Two FPT algorithms are also proposed; the first considers as parameter the treewidth of the input graph and uses exponential space, while the second is parameterized by the size of the minimum
Densest kSubgraph Approximation on Intersection Graphs
"... Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple O ..."
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Cited by 4 (0 self)
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Abstract. We study approximation solutions for the densest ksubgraph problem (DSk) on several classes of intersection graphs. We adopt the concept of σquasi elimination orders, introduced by Akcoglu et al. [1], generalizing the perfect elimination orders for chordal graphs, and develop a simple
PTAS for Densest kSubgraph in Interval Graphs
, 2011
"... Given an interval graph and integer k, we consider the problem of finding a subgraph of size k with a maximum number of induced edges, called densest ksubgraph problem in interval graphs. It has been shown that this problem is NPhard even for chordal graphs [17], and there is probably no PTAS for ..."
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Cited by 4 (0 self)
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Given an interval graph and integer k, we consider the problem of finding a subgraph of size k with a maximum number of induced edges, called densest ksubgraph problem in interval graphs. It has been shown that this problem is NPhard even for chordal graphs [17], and there is probably no PTAS
The densest ksubgraph problem on clique graphs
 IN INTERNATIONAL COMBINATORICS, GEOMETRY AND COMPUTER SCIENCE CONFERENCE
, 2007
"... The Densest kSubgraph (DkS) problem asks for a kvertex subgraph of a given graph with the maximum number of edges. The problem is strongly NPhard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this p ..."
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Cited by 8 (1 self)
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The Densest kSubgraph (DkS) problem asks for a kvertex subgraph of a given graph with the maximum number of edges. The problem is strongly NPhard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS
Approximating the Sparsest kSubgraph in Chordal Graphs
, 2013
"... Given a simple undirected graph G = (V, E) and an integer k < V, the Sparsest kSubgraph problem asks for a set of k vertices which induces the minimum number of edges. As a generalization of the classical independent set problem, Sparsest kSubgraph is N Phard and even not approximable unless ..."
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Cited by 1 (1 self)
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unless P = N P in general graphs. Thus, we investigate Sparsest kSubgraph in graph classes where independent set is polynomialtime solvable, such as subclasses of perfect graphs. Our two main results are the N Phardness of Sparsest kSubgraph on chordal graphs, and a greedy 2approximation algorithm
A deterministic approximation algorithm for the Densest kSubgraph Problem
 International Journal of Operational Research
"... Abstract. In the Densest kSubgraph 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 maximizes the number of edges which have their two endpoints in the subset. This problem is N ..."
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Cited by 7 (0 self)
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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 Densest kSubgraph Problem (where d is the density of G). The complexity of our algorithm is only the one of linear programming
 Detecting High LogDensities – an O(n 1/4) Approximation for Densest kSubgraph.
, 2009
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Results 1  10
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