An O(n log n) Algorithm for Rectilinear Minimal Spanning Trees
Journal of the ACM (JACM)
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Constrained Delaunay triangulations
SCG '87 Proceedings of the third annual symposium on Computational geometry
Construction of multidimensional spanner graphs, with applications to minimum spanning trees
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On the all-pairs Euclidean short path problem
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
Generating low-degree 2-spanners
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A practical algorithm for computing the Delaunay triangulation for convex distance functions
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Sparse communication networks and efficient routing in the plane (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Beta-skeletons have unbounded dilation
Computational Geometry: Theory and Applications
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating k-Spanner Problems for k2
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
On the Spanning Ratio of Gabriel Graphs and beta-skeletons
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The Hardness of Approximating Spanner Problems
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Fault-tolerant geometric spanners
Proceedings of the nineteenth annual symposium on Computational geometry
On greedy geographic routing algorithms in sensing-covered networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Approximating k-spanner problems for k 2
Theoretical Computer Science
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Impact of Sensing Coverage on Greedy Geographic Routing Algorithms
IEEE Transactions on Parallel and Distributed Systems
Geometric spanners with applications in wireless networks
Computational Geometry: Theory and Applications
Analysis of Topology Aggregation techniques for QoS routing
ACM Computing Surveys (CSUR)
Region-fault tolerant geometric spanners
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Local properties of geometric graphs
Computational Geometry: Theory and Applications
I/O-efficient algorithms for computing planar geometric spanners
Computational Geometry: Theory and Applications
A simple and efficient kinetic spanner
Proceedings of the twenty-fourth annual symposium on Computational geometry
Delaunay graphs are almost as good as complete graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Computing the Greedy Spanner in Near-Quadratic Time
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Proceedings of the forty-first annual ACM symposium on Theory of computing
Proceedings of the twenty-fifth annual symposium on Computational geometry
A minimum energy path topology control algorithm for wireless multihop networks
Proceedings of the 2009 International Conference on Wireless Communications and Mobile Computing: Connecting the World Wirelessly
Extensions and limits to vertex sparsification
Proceedings of the forty-second ACM symposium on Theory of computing
Subgraph sparsification and nearly optimal ultrasparsifiers
Proceedings of the forty-second ACM symposium on Theory of computing
Improved multi-criteria spanners for ad-hoc networks under energy and distance metrics
INFOCOM'10 Proceedings of the 29th conference on Information communications
Balancing degree, diameter and weight in Euclidean spanners
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A simulation environment for ad hoc networks using sector subdivision
EUROMICRO-PDP'02 Proceedings of the 10th Euromicro conference on Parallel, distributed and network-based processing
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
kthorder geometric spanners for wireless ad hoc networks
ICDCIT'11 Proceedings of the 7th international conference on Distributed computing and internet technology
Fault tolerant interference-aware topology control for ad hoc wireless networks
ADHOC-NOW'11 Proceedings of the 10th international conference on Ad-hoc, mobile, and wireless networks
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
An optimal-time construction of sparse Euclidean spanners with tiny diameter
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
On generalized diamond spanners
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
The stretch factor of L1- and L∞-delaunay triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Sparse Euclidean Spanners with Tiny Diameter
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
Optimal euclidean spanners: really short, thin and lanky
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Improved multicriteria spanners for Ad-Hoc networks under energy and distance metrics
ACM Transactions on Sensor Networks (TOSN)
New doubling spanners: better and simpler
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Approximated algorithms for the minimum dilation triangulation problem
Journal of Heuristics
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Given a set S of points in the plane, there is a triangulation of S such that a path found within this triangulation has length bounded by a constant times the straight-line distance between the endpoints of the path. Specifically, for any two points a and b of S there is a path along edges of the triangulation with length less than √10 times |ab|, where |ab| is the straight-line Euclidean distance between a and b. Thus, a shortest path in this planar graph is less than about 3 times longer than the corresponding straight-line distance. The triangulation that has this property is the L1 metric Delaunay triangulation for the set 5. This result can be applied to motion planning in the plane. Given a source, a destination, and a set of polygonal obstacles of size n, an &Ogr;(n) size data structure can be used to find a reasonable approximation to the shortest path between the source and the destination in &Ogr;(n log n) time.