Discrete Mathematics - Topics on domination
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A deterministic linear time algorithm for geometric separators and its applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Highly dynamic Destination-Sequenced Distance-Vector routing (DSDV) for mobile computers
SIGCOMM '94 Proceedings of the conference on Communications architectures, protocols and applications
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
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
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Fast estimation of diameter and shortest paths (without matrix multiplication)
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees
Journal of the ACM (JACM)
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Preprocessing an undirected planar network to enable fast approximate distance queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to VLSI Systems
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Geometric Separator Theorems and Applications
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Ad-hoc On-Demand Distance Vector Routing
WMCSA '99 Proceedings of the Second IEEE Workshop on Mobile Computer Systems and Applications
Compact Oracles for Reachability and Approximate Distances in Planar Digraphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
RoamHBA: maintaining group connectivity in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
Compact and Low Delay Routing Labeling Scheme for Unit Disk Graphs
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Compact and low delay routing labeling scheme for Unit Disk Graphs
Computational Geometry: Theory and Applications
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We extend the classic notion of well-separated pair decomposition [10] to the (weighted) unit-disk graph metric: the shortest path distance metric induced by the intersection graph of unit disks. We show that for the unit-disk graph metric of n points in the plane and for any constant c≥1, there exists a c-well-separated pair decomposition with O(n log n) pairs, and the decomposition can be computed in O(n log n) time. We also show that for the unit-ball graph metric in k dimensions where k≥3, there exists a c-well-separated pair decomposition with O(n2-2/k) pairs, and the bound is tight in the worst case. We present the application of the well-separated pair decomposition in obtaining efficient algorithms for approximating the diameter, closest pair, nearest neighbor, center, median, and stretch factor, all under the unit-disk graph metric.