Minimum-cost coverage of point sets by disks
Proceedings of the twenty-second annual symposium on Computational geometry
Optimization problems in multiple-interval graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating geometric coverage problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
Exact and approximate link scheduling algorithms under the physical interference model
Proceedings of the fifth international workshop on Foundations of mobile computing
On the complexity of bandwidth allocation in radio networks
Theoretical Computer Science
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Polynomial Time Approximation Scheme for Connected Vertex Cover in Unit Disk Graph
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximating minimum independent dominating sets in wireless networks
Information Processing Letters
Maximum independent set of rectangles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the Cubicity of AT-Free Graphs and Circular-Arc Graphs
Graph Theory, Computational Intelligence and Thought
Minimum Interference Planar Geometric Topology in Wireless Sensor Networks
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
An Approximation Scheme for Terrain Guarding
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Optimizing active ranges for consistent dynamic map labeling
Computational Geometry: Theory and Applications
PTAS for connected vertex cover in unit disk graphs
Theoretical Computer Science
Shifting Strategy for Geometric Graphs without Geometry
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Optimization problems in multiple-interval graphs
ACM Transactions on Algorithms (TALG)
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
Approximation algorithms for geometric intersection graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Local approximation algorithms for scheduling problems in sensor networks
ALGOSENSORS'07 Proceedings of the 3rd international conference on Algorithmic aspects of wireless sensor networks
Domination in geometric intersection graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Exact and approximation algorithms for geometric and capacitated set cover problems
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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
Minimum vertex cover in rectangle graphs
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Minimum vertex cover in rectangle graphs
Computational Geometry: Theory and Applications
PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs
Journal of Combinatorial Optimization
Bidimensionality and geometric graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
ACM Transactions on Algorithms (TALG)
A randomized algorithm for online unit clustering
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
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
Optimization problems in dotted interval graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
A constant-factor approximation for multi-covering with disks
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computational geometry column 56
ACM SIGACT News
European Journal of Combinatorics
| Hi-index | 0.00 |
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 polynomial-time approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weight) and for the minimum weight vertex cover problem in disk graphs. These are the first known PTASs for $\mathcal{NP}$-hard optimization problems on disk graphs. They are based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible. The PTASs for disk graphs represent a common generalization of previous results for planar graphs and unit disk graphs. They can be extended to intersection graphs of other "disk-like" geometric objects (such as squares or regular polygons), also in higher dimensions.