Complexity of network synchronization
Journal of the ACM (JACM)
A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
Routing with polynomial communication-space trade-off
SIAM Journal on Discrete Mathematics
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Compact routing schemes with low stretch factor (extended abstract)
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Fast Algorithms for Constructing t-Spanners and Paths with Stretch t
SIAM Journal on Computing
Near-Linear Time Construction of Sparse Neighborhood Covers
SIAM Journal on Computing
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
Compact routing with minimum stretch
Journal of Algorithms
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Sparse distance preservers and additive spanners
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
Journal of the ACM (JACM)
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
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
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
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
On the locality of distributed sparse spanner construction
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Approximating Shortest Paths in Graphs
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
ACM Transactions on Algorithms (TALG)
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Additive spanners and (α, β)-spanners
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
Computing graph spanners in small memory: fault-tolerance and streaming
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ACM Transactions on Algorithms (TALG)
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
Sparse spanners vs. compact routing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Multiplicative approximations of random walk transition probabilities
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
ESA'11 Proceedings of the 19th European conference on Algorithms
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
Near linear time (1 + ε)-approximation for restricted shortest paths in undirected graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximate distance oracles with improved preprocessing time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved dynamic algorithms for maintaining approximate shortest paths under deletions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Streaming and fully dynamic centralized algorithms for constructing and maintaining sparse spanners
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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Let k ≥ 2 be an integer. We show that any undirected and unweighted graph G = (V, E) on n vertices has a subgraph G' = (V, E') with O(kn1+1/k) edges such that for any two vertices u, v ∈ V, if δG(u, v) = d, then δG'(u, v) = d+O(d1-1/k-1). Furthermore, we show that such subgraphs can be constructed in O(mn1/k) time, where m and n are the number of edges and vertices in the original graph. We also show that it is possible to construct a weighted graph G* = (V, E*) with O(kn1+1/(2k-1)) edges such that for every u, v ∈ V, if δG(u, v) = d, then δ ≤ δG*(u, v) = d + O(d1-1/k-1). These are the first such results with additive error terms of the form o(d), i.e., additive error terms that are sublinear in the distance being approximated.