A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Efficient message routing in planar networks
SIAM Journal on Computing
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Compact routing with minimum stretch
Journal of Algorithms
Space-efficiency for routing schemes of stretch factor three
Journal of Parallel and Distributed Computing
A data tracking scheme for general networks
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Finding nearest neighbors in growth-restricted metrics
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Distributed object location in a dynamic network
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Routing in distributed networks: overview and open problems
ACM SIGACT News
The intrinsic dimensionality of graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Geometry of Cuts and Metrics
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Name independent routing for growth bounded networks
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Small hop-diameter sparse spanners for doubling metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the topologies formed by selfish peers
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Object location using path separators
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Optimal-stretch name-independent compact routing in doubling metrics
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A doubling dimension threshold θ(loglogn) for augmented graph navigability
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Compact routing with slack in low doubling dimension
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Optimal scale-free compact routing schemes in networks of low doubling dimension
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Ultra-low-dimensional embeddings for doubling metrics
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
Approximating TSP on metrics with bounded global growth
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Hierarchical routing over dynamic wireless networks
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Dynamic routing and location services in metrics of low doubling dimension
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Localized Spanner Construction for Ad Hoc Networks with Variable Transmission Range
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Dynamic Routing and Location Services in Metrics of Low Doubling Dimension
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Using the doubling dimension to analyze the generalization of learning algorithms
Journal of Computer and System Sciences
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
Bounded-hop energy-efficient broadcast in low-dimensional metrics via coresets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
How to complete a doubling metric
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Additive spanners and (α, β)-spanners
ACM Transactions on Algorithms (TALG)
Genus and the geometry of the cut graph
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Balancing degree, diameter and weight in Euclidean spanners
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Fast approximation in subspaces by doubling metric decomposition
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Resilient and low stretch routing through embedding into tree metrics
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Navigating in a Graph by Aid of Its Spanning Tree Metric
SIAM Journal on Discrete Mathematics
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Distance-Sensitive information brokerage in sensor networks
DCOSS'06 Proceedings of the Second IEEE international conference on Distributed Computing in Sensor Systems
Compact routing for graphs excluding a fixed minor
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Sparse fault-tolerant spanners for doubling metrics with bounded hop-diameter or degree
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Distributed and compact routing using spatial distributions in wireless sensor networks
ACM Transactions on Sensor Networks (TOSN)
Optimal euclidean spanners: really short, thin and lanky
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
New doubling spanners: better and simpler
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α if every set of diameter D can be covered by 2α sets of diameter D/2. (A doubling metric is one whose doubling dimension dim(X) is a constant.) We show how to perform (1 + τ)-stretch routing on metrics for any 0 T ≤ 1 with routing tables of size at most (α/τ)O(α) log2 Δ bits with only (α/τ)O(α) log Δ entries, where Δ is the diameter of the graph; hence the number of routing table entries is just τ-O(1) log Δ for doubling metrics. These results extend and improve on those of Talwar (2004).We also give better constructions of sparse spanners for doubling metrics than those obtained from the routing tables above; for τ 0, we give algorithms to construct (1 + τ)-stretch spanners for a metric (X, d) with maximum degree at most (2 + 1/τ)O(dim(X)), matching the results of Das et al. for Euclidean metrics.