Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for the bottleneck stretch factor problem
Nordic Journal of Computing
Approximation Algorithms for the Bottleneck Stretch Factor Problem
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
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
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
A Fast Algorithm for Approximating the Detour of a Polygonal Chain
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Well-separated pair decomposition for the unit-disk graph metric and its applications
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Spatiotemporal multicast in sensor networks
Proceedings of the 1st international conference on Embedded networked sensor systems
A fast algorithm for approximating the detour of a polygonal chain
Computational Geometry: Theory and Applications
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Finding the best shortcut in a geometric network
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The bin-covering technique for thresholding random geometric graph properties
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Many distances in planar graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The density of iterated crossing points and a gap result for triangulations of finite point sets
Proceedings of the twenty-second annual symposium on Computational geometry
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Deformable spanners and applications
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Local Construction and Coloring of Spanners of Location Aware Unit Disk Graphs
Graph-Theoretic Concepts in Computer Science
On the dilation spectrum of paths, cycles, and trees
Computational Geometry: Theory and Applications
Algorithms for graphs of bounded treewidth via orthogonal range searching
Computational Geometry: Theory and Applications
Connect the Dot: Computing Feed-Links with Minimum Dilation
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Deformable spanners and applications
Computational Geometry: Theory and Applications
Error scaling laws for linear optimal estimation from relative measurements
IEEE Transactions on Information Theory
Dilation-optimal edge deletion in polygonal cycles
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Thresholding random geometric graph properties motivated by ad hoc sensor networks
Journal of Computer and System Sciences
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
More Algorithms for All-Pairs Shortest Paths in Weighted Graphs
SIAM Journal on Computing
Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees
SIAM Journal on Discrete Mathematics
Property testing
Property testing
Constructing interference-minimal networks
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
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
Fast pruning of geometric spanners
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
The emergence of sparse spanners and greedy well-separated pair decomposition
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Local construction of planar spanners in unit disk graphs with irregular transmission ranges
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Approximated algorithms for the minimum dilation triangulation problem
Journal of Heuristics
| Hi-index | 0.06 |
There are several results available in the literature dealing with efficient construction of t-spanners for a given set S of n points in $\IR^d$. t-spanners are Euclidean graphs in which distances between vertices in G are at most t times the Euclidean distances between them; in other words, distances in G are "stretched" by a factor of at most t. We consider the interesting dual problem: given a Euclidean graph G whose vertex set corresponds to the set S, compute the stretch factor of G, i.e., the maximum ratio between distances in G and the corresponding Euclidean distances. It can trivially be solved by solving the all-pairs-shortest-path problem. However, if an approximation to the stretch factor is sufficient, then we show it can be efficiently computed by making only O(n) approximate shortest path queries in the graph G. We apply this surprising result to obtain efficient algorithms for approximating the stretch factor of Euclidean graphs such as paths, cycles, trees, planar graphs, and general graphs. The main idea behind the algorithm is to use Callahan and Kosaraju's well-separated pair decomposition.