Results 1  10
of
104
Simple heuristics for unit disk graphs
 NETWORKS
, 1995
"... Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NPhard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring ..."
Abstract

Cited by 151 (6 self)
 Add to MetaCart
Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NPhard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum
Approximation algorithms for unit disk graphs
 IN PROCEEDINGS OF THE 31ST INTERNATIONAL WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE
, 2005
"... Mobile ad hoc networks are frequently modeled by unit disk graphs. We consider several classical graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set), which are relevant to such networks. We propose two new notions for u ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Mobile ad hoc networks are frequently modeled by unit disk graphs. We consider several classical graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set), which are relevant to such networks. We propose two new notions
Densest kSubgraph Approximation on Intersection Graphs
"... 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(σ)appro ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
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(σ)approximation
PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
Abstract

Cited by 102 (5 self)
 Add to MetaCart
A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total
Maximal Cliques in Unit Disk Graphs: Polynomial Approximation
 IN PROCEEDINGS INOC 2005
, 2005
"... We consider the problem of generating all maximal cliques in an unit disk graph. General algorithms to find all maximal cliques are exponential, so we rely on a polynomial approximation. Our algorithm makes use of certain key geographic structures of these graphs. For each edge, we limit the set of ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We consider the problem of generating all maximal cliques in an unit disk graph. General algorithms to find all maximal cliques are exponential, so we rely on a polynomial approximation. Our algorithm makes use of certain key geographic structures of these graphs. For each edge, we limit the set
LinearTime Approximation Algorithms for Unit Disk Graphs
"... Numerous approximation algorithms for unit disk graphs have been proposed in the literature, exhibiting sharp tradeoffs between running times and approximation ratios. We propose a method to obtain lineartime approximation algorithms for unit disk graph problems. Our method yields lineartime (4 + ..."
Abstract
 Add to MetaCart
Numerous approximation algorithms for unit disk graphs have been proposed in the literature, exhibiting sharp tradeoffs between running times and approximation ratios. We propose a method to obtain lineartime approximation algorithms for unit disk graph problems. Our method yields lineartime (4
A robust ptas for maximum weight independent sets in unit disk graphs
 In WG
, 2004
"... Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomialtime approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geo ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
Abstract. A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomialtime approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a
Hierarchically Specified Unit Disk Graphs
, 1995
"... We characterize the complexity of a number of basic optimization problems for unit disk graphs specified hierarchically as in [BOW83, LW87a, Le88, LW92]. Both PSPACEhardness results and polynomial time approximations are presented for most of the problems considered. These problems include minim ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
We characterize the complexity of a number of basic optimization problems for unit disk graphs specified hierarchically as in [BOW83, LW87a, Le88, LW92]. Both PSPACEhardness results and polynomial time approximations are presented for most of the problems considered. These problems include
MAXIMUM AREA INDEPENDENT SETS IN DISK INTERSECTION GRAPHS
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
, 2008
"... Maximum Independent Set (MIS) and its relative Maximum Weight Independent Set (MWIS) are wellknown problems in combinatorial optimization; they are NPhard even in the geometric setting of unit disk graphs. In this paper, we study the Maximum Area Independent Set (MAIS) problem, a natural restric ..."
Abstract

Cited by 6 (6 self)
 Add to MetaCart
restricted version of MWIS in disk intersection graphs where the weight equals the disk area. We obtain: (i) Quantitative bounds on the maximum total area of an independent set relative to the union area; (ii) Practical constantratio approximation algorithms for finding an independent set with a large total
Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs
, 2000
"... . Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is defined on a slab whose width is k, we propose an algorithm for finding a maximum independent set ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
set in O(n 4d2k= p 3e ) time where n denotes the number of vertices. We also propose a (1 0 1=r)approximation algorithm for the maximum independent set problems on a (general) unit disk graph whose time complexity is bounded by O(rn 4d2(r01)= p 3e ). We also propose an algorithm
Results 1  10
of
104