Fast algorithms for finding nearest common ancestors
SIAM Journal on Computing
On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
An optimal algorithm for constructing oriented Voronoi diagrams and geographic neighborhood graphs
Information Processing Letters
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Introduction to Algorithms
Approximation algorithms for the bottleneck stretch factor problem
Nordic Journal of Computing
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On-Line Algorithms for Shortest Path Problems on Planar Digraphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Efficient cluster compensation for lin-kernighan heuristics
Efficient cluster compensation for lin-kernighan heuristics
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Bounded-leg distance and reachability oracles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
On Spanners and Lightweight Spanners of Geometric Graphs
SIAM Journal on Computing
On a family of strong geometric spanners that admit local routing strategies
Computational Geometry: Theory and Applications
Undirected connectivity of sparse Yao graphs
FOMC '11 Proceedings of the 7th ACM ACM SIGACT/SIGMOBILE International Workshop on Foundations of Mobile Computing
Path minima queries in dynamic weighted trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Communication-efficient construction of the plane localized delaunay graph
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Randomized AB-Face-AB routing algorithms in mobile ad hoc networks
ADHOC-NOW'05 Proceedings of the 4th international conference on Ad-Hoc, Mobile, and Wireless Networks
Diamond triangulations contain spanners of bounded degree
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
On bounded degree plane strong geometric spanners
Journal of Discrete Algorithms
On a family of strong geometric spanners that admit local routing strategies
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Spanners for geometric intersection graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: given two points p and q of S and a real number L, compute (or approximate) a shortest path between p and q in the subgraph of the complete graph on S consisting of all edges whose lengths are less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on Euclidean minimum spanning trees, spanners, and the Delaunay triangulation. A result of independent interest is the following. For any two points p and q of S, there is a path between p and q in the Delaunay triangulation, whose length is less than or equal to 2π/(3 cos(π/6)) times the Euclidean distance |pq| between p and q, and all of whose edges have length at most |pq|.