Approximating the complete Euclidean graph
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Approximate Distance Oracles Revisited
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
t-Spanners as a Data Structure for Metric Space Searching
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Computing the Maximum Detour and Spanning Ratio of Planar Paths, Trees, and Cycles
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Geometric Spanners for Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Spanners and message distribution in networks
Discrete Applied Mathematics - Special issue on international workshop on algorithms, combinatorics, and optimization in interconnection networks (IWACOIN '99)
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast pruning of geometric spanners
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Connect the Dot: Computing Feed-Links with Minimum Dilation
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Almost all Delaunay triangulations have stretch factor greater than π/2
Computational Geometry: Theory and Applications
Property testing
Property testing
Exact and approximation algorithms for computing the dilation spectrum of paths, trees, and cycles
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Max-stretch reduction for tree spanners
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
| Hi-index | 0.00 |
Given a Euclidean graph G in Rd with n vertices and m edges we consider the problem of adding a shortcut such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a Euclidean graph runs in O(mn+n2 log n) time, resulting in a trivial O(mn3+n4 log n) time algorithm for computing the optimal shortcut. First, we show that a simple modification yields the optimal solution in O(n4) time using O(n2) space. To reduce the running times we consider several approximation algorithms. Our main result is a (2+ε)-approximation algorithm with running time O(nm+n2(log n+1/ε3d)) using O(n2) space.