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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
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
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
A constant approximation algorithm for the densest ksubgraph problem on chordal graphs
, 2008
"... ..."
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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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
DOI 10.1007/s1087800790691 The densest ksubgraph problem on clique graphs
, 2007
"... Abstract 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 ..."
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Abstract 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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. Finally, we also show how to derive a P T AS for Sparsest kSubgraph on proper interval graphs.
Detecting High LogDensities – an O(n 1/4) Approximation for Densest kSubgraph
"... In the Densest kSubgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower bounds for this problem. It is NPhard, and does not have a PTAS ..."
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Cited by 23 (1 self)
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In the Densest kSubgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower bounds for this problem. It is NPhard, and does not have a PTAS
Parameterized Complexity of the Sparsest kSubgraph Problem in Chordal Graphs?
"... Abstract. In this paper we study the Sparsest kSubgraph problem which consists in finding a subset of k vertices in a graph which induces the minimum number of edges. The Sparsest kSubgraph problem is a natural generalization of the Independent Set problem, and thus is NPhard (and even W [1]hard ..."
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]hard) in general graphs. In this paper we investigate the parameterized complexity of both Sparsest kSubgraph and Densest kSubgraph in chordal graphs. We first provide simple proofs that Densest kSubgraph in chordal graphs is FPT and does not admit a polynomial kernel unlessNP ⊆ coNP/poly (both
Results 1  10
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34,417