Complexity of network synchronization
Journal of the ACM (JACM)
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
An optimal synchronizer for the hypercube
PODC '87 Proceedings of the sixth annual ACM Symposium on Principles of distributed computing
An optimal synchronizer for the hypercube
SIAM Journal on Computing
Locality in distributed graph algorithms
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
On the complexity of distributed network decomposition
Journal of Algorithms
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
All-Pairs Almost Shortest Paths
SIAM Journal on Computing
(1 + &egr;&Bgr;)-spanner constructions for general graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
$(1 + \epsilon,\beta)$-Spanner Constructions for General Graphs
SIAM Journal on Computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Efficient algorithms for constructing (1+,ε, β)-spanners in the distributed and streaming models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Journal of the ACM (JACM)
New constructions of (α, β)-spanners and purely additive spanners
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Computing almost shortest paths
ACM Transactions on Algorithms (TALG)
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Sparse Distance Preservers and Additive Spanners
SIAM Journal on Discrete Mathematics
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
Geometric Spanner Networks
Roundtrip spanners and roundtrip routing in directed graphs
ACM Transactions on Algorithms (TALG)
Proximity-preserving labeling schemes
Journal of Graph Theory
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
Fault-tolerant spanners for general graphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Remote-spanners: What to know beyond neighbors
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
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
All-pairs nearly 2-approximate shortest-paths in O(n2 polylog n) time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Towards a complexity theory for local distributed computing
Journal of the ACM (JACM)
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An (α, β)-spanner of a graph G is a subgraph H that approximates distances in G within a multiplicative factor α and an additive error β, ensuring that for any two nodes u, v, dH(u, v) ≤ α ċ dG(u, v)+β. This paper concerns algorithms for the distributed deterministic construction of a sparse (α, β)-spanner H for a given graph G and distortion parameters α and β. It first presents a generic distributed algorithm that in constant number of rounds constructs, for every n-node graph and integer k ≥ 1, an (α, β)-spanner of O(βn1+1/k) edges, where α and β are constants depending on k. For suitable parameters, this algorithm provides a (2k - 1, 0)-spanner of at most kn1+1/k edges in k rounds, matching the performances of the best known distributed algorithm by Derbel et al. (PODC '08). For k = 2 and constant Ɛ 0, it can also produce a (1 + Ɛ, 2 - Ɛ)-spanner of O(n3/2) edges in constant time. More interestingly, for every integer k 1, it can construct in constant time a (1 + Ɛ, O(1/Ɛ)k-2)-spanner of O(Ɛ-k+1n1+1/k) edges. Such deterministic construction was not previously known. The paper also presents a second generic deterministic and distributed algorithm based on the construction of small dominating sets and maximal independent sets. After computing such sets in sub-polynomial time, it constructs at its best a (1 + Ɛ, β)-spanner with O(βn1+1/k) edges, where β = klog(log k/Ɛ)+O(1). For k = 3, it provides a (1 + Ɛ, 6 - Ɛ)-spanner with O(Ɛ-1n4/3) edges. The additive terms β = β(k, Ɛ) in the stretch of our constructions yield the best trade-off currently known between k and Ɛ, due to Elkin and Peleg (STOC '01). Our distributed algorithms are rather short, and can be viewed as a unification and simplification of previous constructions.