Locality in distributed graph algorithms
SIAM Journal on Computing
Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Topology control and routing in ad hoc networks: a survey
ACM SIGACT News
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
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
Fault-Tolerant Geometric Spanners
Discrete & Computational Geometry
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
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Small hop-diameter sparse spanners for doubling metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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
The MST of symmetric disk graphs (in arbitrary metric spaces) is light
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The MST of Symmetric Disk Graphs (in Arbitrary Metric Spaces) is Light
SIAM Journal on Discrete Mathematics
| Hi-index | 0.00 |
This paper presents a distributed algorithm that runs on an n-node unit ball graph (UBG) G residing in a metric space of constant doubling dimension, and constructs, for any ε 0, a (1 + ε)-spanner H of G with maximum degree bounded above by a constant. In addition, we show that H is “lightweight”, in the following sense. Let Δ denote the aspect ratio of G, that is, the ratio of the length of a longest edge in G to the length of a shortest edge in G. The total weight of H is bounded above by O(logΔ) · wt(MST), where MST denotes a minimum spanning tree of the metric space. Finally, we show that H satisfies the so called leapfrog property, an immediate implication being that, for the special case of Euclidean metric spaces with fixed dimension, the weight of H is bounded above by O(wt(MST)). Thus, the current result subsumes the results of the authors in PODC 2006 that apply to Euclidean metric spaces, and extends these results to metric spaces with constant doubling dimension.