A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
New sparseness results on graph spanners
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Highly dynamic Destination-Sequenced Distance-Vector routing (DSDV) for mobile computers
SIGCOMM '94 Proceedings of the conference on Communications architectures, protocols and applications
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Space-time tradeoff for answering range queries (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Ad-hoc On-Demand Distance Vector Routing
WMCSA '99 Proceedings of the Second IEEE Workshop on Mobile Computer Systems and Applications
A Highly Adaptive Distributed Routing Algorithm for Mobile Wireless Networks
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
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
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Compact routing on euclidian metrics
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On hierarchical routing in doubling metrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Proximity algorithms for nearly-doubling spaces
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Balancing degree, diameter and weight in Euclidean spanners
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
An optimal-time construction of sparse Euclidean spanners with tiny diameter
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete 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
| Hi-index | 0.00 |
Given a metric M = (V, d), a graph G = (V, E) is a t-spanner for M if every pair of nodes in V has a "short" path (i.e., of length at most t times their actual distance) between them in the spanner. Furthermore, this spanner has a hop diameter bounded by D if every such short path also uses at most D edges. We consider the problem of constructing sparse (1 + ε)-spanners with small hop diameter for metrics of low doubling dimension.In this paper, we show that given any metric with constant doubling dimension k, and any 0 O(n log* n + nε-O(k)) edges) and a constant hop diameter, and also a (1 + ε)-spanner with linear number of edges (i.e., only nε-O(k) edges) which achieves a hop diameter that grows like the functional inverse of the Ackermann's function. Moreover, we prove that such tradeoffs between the number of edges and the hop diameter are asymptotically optimal.