There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Minimum spanning trees in k-dimensional space
SIAM Journal on Computing
Approximating the complete Euclidean graph
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Journal of Algorithms
Fault-tolerant geometric spanners
Proceedings of the nineteenth annual symposium on Computational geometry
A Divide-and-Conquer Algorithm for Min-Cost Perfect Matching in the Plane
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Geometric Spanner Networks
A simple and efficient kinetic spanner
Proceedings of the twenty-fourth annual symposium on Computational geometry
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
On the Power of the Semi-Separated Pair Decomposition
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A simple and efficient kinetic spanner
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We introduce the concept of region-fault tolerant spanners for planar point sets, and prove the existence of region-fault tolerant spanners of small size. For a geometric graph G on a point set P and a region F, we define G ⊖ F to be what remains of G after the vertices and edges of G intersecting F have been removed. A C-fault tolerant t-spanner is a geometric graph G on P such that for any convex region F, the graph G ⊖ F is a t-spanner for Gc(P)⊖F, where Gc(P) is the complete geometric graph on P. We prove that any set P of n points admits a C-fault tolerant (1 + ε)-spanner of size O(n log n), for any constant ε 0; if adding Steiner points is allowed then the size of the spanner reduces to O(n), and for several special cases we show how to obtain region-fault tolerant spanners of O(n) size without using Steiner points. We also consider fault-tolerant geodesic t-spanners: this is a variant where, for any disk D, the distance in G ⊖ D between any two points u, v ε P \ D is at most t times the geodesic distance between u and v in R2 \ D. We prove that for any P we can add O(n) Steiner points to obtain a fault-tolerant geodesic (1 + ε)-spanner of size O(n).