Discrete Mathematics - Topics on domination
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Intersection Graphs of Noncrossing Arc-Connected Sets in the Plane
GD '96 Proceedings of the Symposium on Graph Drawing
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Ad-hoc networks beyond unit disk graphs
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Robust algorithms for restricted domains
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
A PTAS for the minimum dominating set problem in unit disk graphs
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
A robust PTAS for maximum weight independent sets in unit disk graphs
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Distributed Sleep Scheduling in Wireless Sensor Networks via Fractional Domatic Partitioning
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Shifting Strategy for Geometric Graphs without Geometry
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Distributed algorithms for approximating wireless network capacity
INFOCOM'10 Proceedings of the 29th conference on Information communications
Polynomial time approximation schemes for minimum disk cover problems
Journal of Combinatorial Optimization
Approximation algorithms for intersection graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A weakly robust PTAS for minimum clique partition in unit disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
PTAS for the minimum weighted dominating set in growth bounded graphs
Journal of Global Optimization
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Wireless networks are created by the communication links between a collection of radio transceivers. The nature of wireless transmissions does not lead to arbitrary undirected graphs but to structured graphs which we characterize by the polynomially bounded growth property. In contrast to many existing graph models for wireless networks, the property of polynomially bounded growth is defined independently of geometric data such as positional information. On such wireless networks, we present an approach that can be used to create polynomial-time approximation schemes for several optimization problems called the local neighborhood-based scheme. We apply this approach to the problems of seeking maximum (weight) independent sets and minimum dominating sets. These are two important problems in the area of wireless communication networks and are also used in many applications ranging from clustering to routing strategies. However, the approach is presented in a general fashion since it can be applied to other problems as well. The approach for the approximation schemes is robust in the sense that it accepts any undirected graph as input and either outputs a solution of desired quality or correctly asserts that the graph presented as input does not satisfy the structural assumption of a wireless network (an NP-hard problem).