Preprocessing an undirected planar network to enable fast approximate distance queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Algorithms for Finding Level Ancestors in Dynamic Trees
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Dynamic Approximate All-Pairs Shortest Paths in Undirected Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Journal of the ACM (JACM)
SIAM Journal on Computing
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Ramsey partitions and proximity data structures
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Faster Algorithms for Approximate Distance Oracles and All-Pairs Small Stretch Paths
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Approximate distance oracles for unweighted graphs in expected O(n2) time
ACM Transactions on Algorithms (TALG)
Fully dynamic geometric spanners
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Embedding metric spaces in their intrinsic dimension
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved algorithms for fully dynamic geometric spanners and geometric routing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Dynamic Spanner for Doubling Metric Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A constructive proof of the general lovász local lemma
Journal of the ACM (JACM)
Distance Oracles for Sparse Graphs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
ESA'11 Proceedings of the 19th European conference on Algorithms
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
| Hi-index | 0.02 |
We present an approximate distance oracle for a point set S with n points and doubling dimension λ. For every ε 0, the oracle supports (1 + ε)-approximate distance queries in (universal) constant time, occupies space [ε−O(λ) + 2O(λ log λ)]n, and can be constructed in [2O(λ) log3 n + ε−O(λ) +2O(λ log λ)]n expected time. This improves upon the best previously known constructions, presented by Har-Peled and Mendel [13]. Furthermore, the oracle can be made fully dynamic with expected O(1) query time and only 2O(λ) log n + ε−O(λ) +2O(λ log λ) update time. This is the first fully dynamic (1 + ε)-distance oracle.