The input/output complexity of sorting and related problems
Communications of the ACM
A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Extremal graphs with no C4,s, or C10,s
Journal of Combinatorial Theory Series B
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
On sparse spanners of weighted graphs
Discrete & Computational Geometry
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Polylog-time and near-linear work approximation scheme for undirected shortest paths
Journal of the ACM (JACM)
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Compact roundtrip routing in directed networks
Journal of Algorithms
Approximating Minimum Max-Stretch spanning Trees on unweighted graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Journal of the ACM (JACM)
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sparse source-wise and pair-wise distance preservers
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
New constructions of (α, β)-spanners and purely additive spanners
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
Approximating k-spanner problems for k 2
Theoretical Computer Science
Metric Embeddings with Relaxed Guarantees
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Small hop-diameter sparse spanners for doubling metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On space-stretch trade-offs: upper bounds
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Lower Bounds for Additive Spanners, Emulators, and More
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)
Geometric Spanner Networks
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Embedding metrics into ultrametrics and graphs into spanning trees with constant average distortion
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Distance Oracles for Unweighted Graphs: Breaking the Quadratic Barrier with Constant Additive Error
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Deterministic constructions of approximate distance oracles and spanners
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
ACM Transactions on Algorithms (TALG)
Additive spanners in nearly quadratic time
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
On approximate distance labels and routing schemes with affine stretch
DISC'11 Proceedings of the 25th international conference on Distributed computing
Spectral sparsification via random spanners
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Fault tolerant additive spanners
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Efficient distributed source detection with limited bandwidth
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Small stretch pairwise spanners
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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An (α, β)-spanner of an unweighted graph G is a subgraph H that distorts distances in G up to a multiplicative factor of α and an additive term β. It is well known that any graph contains a (multiplicative) (2k−1, 0)-spanner of size O(n1+1/k) and an (additive) (1,2)-spanner of size O(n3/2). However no other additive spanners are known to exist. In this article we develop a couple of new techniques for constructing (α, β)-spanners. Our first result is an additive (1,6)-spanner of size O(n4/3). The construction algorithm can be understood as an economical agent that assigns costs and values to paths in the graph, purchasing affordable paths and ignoring expensive ones, which are intuitively well approximated by paths already purchased. We show that this path buying algorithm can be parameterized in different ways to yield other sparseness-distortion tradeoffs. Our second result addresses the problem of which (α, β)-spanners can be computed efficiently, ideally in linear time. We show that, for any k, a (k,k−1)-spanner with size O(kn1+1/k) can be found in linear time, and, further, that in a distributed network the algorithm terminates in a constant number of rounds. Previous spanner constructions with similar performance had roughly twice the multiplicative distortion.