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
Lower bounds for graph embeddings and combinatorial preconditioners
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Tradeoffs between stretch factor and load balancing ratio in routing on growth restricted graphs
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of 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 distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On hierarchical routing in doubling metrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Name independent routing for growth bounded networks
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Meridian: a lightweight network location service without virtual coordinates
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Near-optimal sensor placements: maximizing information while minimizing communication cost
Proceedings of the 5th international conference on Information processing in sensor networks
Searching dynamic point sets in spaces with bounded doubling dimension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The black-box complexity of nearest-neighbor search
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Energy conservation via domatic partitions
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Cover trees for nearest neighbor
ICML '06 Proceedings of the 23rd international conference on Machine learning
Optimal-stretch name-independent compact routing in doubling metrics
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Metric structures in L1: dimension, snowflakes, and average distortion
European Journal of Combinatorics
Deformable spanners and applications
Computational Geometry: Theory and Applications
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Vertex cuts, random walks, and dimension reduction in series-parallel graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Nearest-neighbor-preserving embeddings
ACM Transactions on Algorithms (TALG)
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
Embedding metric spaces in their intrinsic dimension
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
Clustering for metric and non-metric distance measures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Metric clustering via consistent labeling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Ranged hash functions and the price of churn
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Embeddings of negative-type metrics and an improved approximation to generalized sparsest cut
ACM Transactions on Algorithms (TALG)
Random projection trees and low dimensional manifolds
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hierarchical routing over dynamic wireless networks
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
Recovering the Long-Range Links in Augmented Graphs
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Dimensions of Points in Self-similar Fractals
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Space-Time Tradeoffs for Proximity Searching in Doubling Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Optimal Dynamic Spanner for Doubling Metric Spaces
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Dynamic Routing and Location Services in Metrics of Low Doubling Dimension
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
On the internet delay space dimensionality
Proceedings of the 8th ACM SIGCOMM conference on Internet measurement
Graph Augmentation via Metric Embedding
OPODIS '08 Proceedings of the 12th International Conference on Principles of Distributed Systems
Using the doubling dimension to analyze the generalization of learning algorithms
Journal of Computer and System Sciences
Triangulation and embedding using small sets of beacons
Journal of the ACM (JACM)
Distributed resource management and matching in sensor networks
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
On the Optimality of Gluing over Scales
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Deformable spanners and applications
Computational Geometry: Theory and Applications
Nonmyopic adaptive informative path planning for multiple robots
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Ultra-low-dimensional embeddings for doubling metrics
Journal of the ACM (JACM)
Recovering the long-range links in augmented graphs
Theoretical Computer Science
Hard metrics from Cayley graphs of Abelian groups
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
Minimum-energy broadcast with few senders
DCOSS'07 Proceedings of the 3rd IEEE international conference on Distributed computing in sensor systems
How to complete a doubling metric
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
New constructions of SSPDs and their applications
Proceedings of the twenty-sixth annual symposium on Computational geometry
Distributed averaging via lifted Markov chains
IEEE Transactions on Information Theory
Clustering for metric and nonmetric distance measures
ACM Transactions on Algorithms (TALG)
Forbidden-set distance labels for graphs of bounded doubling dimension
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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
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
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Estimating the average of a Lipschitz-continuous function from one sample
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Bayesian active learning using arbitrary binary valued queries
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Algorithmic models for sensor networks
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Robust sensor placements at informative and communication-efficient locations
ACM Transactions on Sensor Networks (TOSN)
A Lower Bound for Network Navigability
SIAM Journal on Discrete Mathematics
Near-optimal distortion bounds for embedding doubling spaces into L1
Proceedings of the forty-third annual ACM symposium on Theory of computing
Fault-tolerant spanners: better and simpler
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Randomized compact routing in decomposable metrics
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Low distortion metric embedding into constant dimension
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Resilient and low stretch routing through embedding into tree metrics
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Bandwidth and low dimensional embedding
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Metric anomaly detection via asymmetric risk minimization
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Dimension reduction for finite trees in l1
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Distance-Sensitive information brokerage in sensor networks
DCOSS'06 Proceedings of the Second IEEE international conference on Distributed Computing in Sensor Systems
Distance labeling in hyperbolic graphs
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Fast, precise and dynamic distance queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximate nearest neighbor search for low dimensional queries
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Dimensionality reduction: beyond the Johnson-Lindenstrauss bound
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A nonlinear approach to dimension reduction
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
New constructions of SSPDs and their applications
Computational Geometry: Theory and Applications
The emergence of sparse spanners and greedy well-separated pair decomposition
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Compact routing for graphs excluding a fixed minor
DISC'05 Proceedings of the 19th international conference on Distributed Computing
The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Multi-way spectral partitioning and higher-order cheeger inequalities
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A tree-based regressor that adapts to intrinsic dimension
Journal of Computer and System Sciences
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)
Graph cluster randomization: network exposure to multiple universes
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
A node-capacitated okamura-seymour theorem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Optimal euclidean spanners: really short, thin and lanky
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Ranked bandits in metric spaces: learning diverse rankings over large document collections
The Journal of Machine Learning Research
Bandwidth and low dimensional embedding
Theoretical Computer Science
Efficient regression in metric spaces via approximate lipschitz extension
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
New doubling spanners: better and simpler
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
| Hi-index | 0.07 |
The doubling constant of a metric space (X, d) is the smallest value \lambda such that every ball in X can be covered by \lambda balls of half the radius. The doubling dimension of X is then defined as \dim (X) = \log _2 \lambda. A metric (or sequence of metrics) is called doubling precisely when its doubling dimension is bounded. This is a robust class of metric spaces which contains many families of metrics that occur in applied settings.We give tight bounds for embedding doubling metrics into (low-dimensional) normed spaces. We consider both general doubling metrics, as well as more restricted families such as those arising from trees, from graphs excluding a fixed minor, and from snowflaked metrics. Our techniques include decomposition theorems for doubling metrics, and an analysis of a fractal in the plane due to Laakso [21]. Finally, we discuss some applications and point out a centralopen question regarding dimensionality reduction in L2.