Proving geometric algorithm non-solvability: An application of factoring polynomials
Journal of Symbolic Computation
The algebraic degree of geometric optimization problems
Discrete & Computational Geometry
Minimizing the sum of diameters efficiently
Computational Geometry: Theory and Applications
Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Wireless information networks
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Approximation algorithms for lawn mowing and milling
Computational Geometry: Theory and Applications
Clustering to minimize the sum of cluster diameters
Journal of Computer and System Sciences - STOC 2001
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Searching with an autonomous robot
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks and ISDN Systems
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Algorithms for two-box covering
Proceedings of the twenty-second annual symposium on Computational geometry
On clustering to minimize the sum of radii
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
On Metric Clustering to Minimize the Sum of Radii
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Covering a line segment with variable radius discs
Computers and Operations Research
Cheap or Flexible Sensor Coverage
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
A Scheme for Computing Minimum Covers within Simple Regions
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Minimum Covering with Travel Cost
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Locating facilities on a network to minimize their average service radius
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Deploying mesh nodes under non-uniform propagation
INFOCOM'10 Proceedings of the 29th conference on Information communications
Some variations on constrained minimum enclosing circle problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Connecting a set of circles with minimum sum of radii
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Partitioning the nodes of a graph to minimize the sum of subgraph radii
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Radar placement along banks of river
Journal of Global Optimization
More is more: The benefits of denser sensor deployment
ACM Transactions on Sensor Networks (TOSN)
Minimum covering with travel cost
Journal of Combinatorial Optimization
On Clustering to Minimize the Sum of Radii
SIAM Journal on Computing
Providing and finding k-road-coverage efficiently in wireless sensor networks
Wireless Communications & Mobile Computing
A note on multicovering with disks
Computational Geometry: Theory and Applications
Some variations on constrained minimum enclosing circle problem
Journal of Combinatorial Optimization
A note on minimum-sum coverage by aligned disks
Information Processing Letters
| Hi-index | 0.00 |
We consider a class of geometric facility location problems in which the goal is to determine a set X of disks given by their centers (tj) and radii (rj) that cover a given set of demand points Y∈R2 at the smallest possible cost. We consider cost functions of the form Εjf(rj), where f(r)=rα is the cost of transmission to radius r. Special cases arise for α=1 (sum of radii) and α=2 (total area); power consumption models in wireless network design often use an exponent α2. Different scenarios arise according to possible restrictions on the transmission centers tj, which may be constrained to belong to a given discrete set or to lie on a line, etc.We obtain several new results, including (a) exact and approximation algorithms for selecting transmission points tj on a given line in order to cover demand points Y∈R2; (b) approximation algorithms (and an algebraic intractability result) for selecting an optimal line on which to place transmission points to cover Y; (c) a proof of NP-hardness for a discrete set of transmission points in R2 and any fixed α1; and (d) a polynomial-time approximation scheme for the problem of computing a minimum cost covering tour (MCCT), in which the total cost is a linear combination of the transmission cost for the set of disks and the length of a tour/path that connects the centers of the disks.