Discrete Mathematics - Topics on domination
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Improved Tree Decomposition Based Algorithms for Domination-like Problems
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete 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
Parameterized Complexity
On the Cubicity of AT-Free Graphs and Circular-Arc Graphs
Graph Theory, Computational Intelligence and Thought
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
The MST of symmetric disk graphs (in arbitrary metric spaces) is light
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Geometric representation of graphs in low dimension
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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
Algorithms for the minimum weight k-fold (connected) dominating set problem
Journal of Combinatorial Optimization
The MST of Symmetric Disk Graphs (in Arbitrary Metric Spaces) is Light
SIAM Journal on Discrete Mathematics
Connected dominating sets on dynamic geometric graphs
Computational Geometry: Theory and Applications
Optimization problems in dotted interval graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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We consider several graph theoretic problems on unit disk graphs (Maximum Independent Set, Minimum Vertex Cover, and Minimum (Connected) Dominating Set) relevant to mobile ad hoc networks. We propose two new notions: thickness and density. If the thickness of a unit disk graph is bounded, then the mentioned problems can be solved in polynomial time. For unit disk graphs of bounded density, we present a new asymptotic fully-polynomial approximation scheme for the considered problems. The scheme for Minimum Connected Dominating Set is the first Baker-like asymptotic FPTAS for this problem. By adapting the proof, it implies e.g. an asymptotic FPTAS for Minimum Connected Dominating Set on planar graphs.