Complexity of network synchronization
Journal of the ACM (JACM)
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
On the complexity of distributed network decomposition
Journal of Algorithms
Fast distributed network decompositions and covers
Journal of Parallel and 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
Simple and efficient network decomposition and synchronization
Theoretical Computer Science
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
Computing almost shortest paths
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Roundtrip spanners and roundtrip routing in directed graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Compact routing schemes with low stretch factor
Journal of Algorithms
Approximate distance oracles for unweighted graphs in Õ (n2) time
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
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
Journal of Algorithms
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
Spanners and emulators with sublinear distance errors
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons
Journal of Computer and System Sciences
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & Algorithms
Network decomposition and locality in distributed computation
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Near-linear cost sequential and distributed constructions of sparse neighborhood covers
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Fast distributed graph partition and application
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Fast deterministic distributed algorithms for sparse spanners
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
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
Fast deterministic distributed algorithms for sparse spanners
Theoretical Computer Science
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
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The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n3/2) edge 3- spanner for it in O(log n) time. This algorithm is then extended into a deterministic algorithm for computing an O(k n1+1/k) edge O(k)-spanner in 2O(k) logk-1 n time for every integer parameter k ≥ 1. This establishes that the problem of the deterministic construction of a linear (in k) stretch spanner with few edges can be solved in the distributed setting in polylogarithmic time. The paper also investigates the distributed construction of sparse spanners with almost pure additive stretch (1 + ε, β), i.e., such that the distance in the spanner is at most 1 + ε times the original distance plus β. It is shown, for every ε 0, that in O(ε-1 log n) time one can deterministically construct a spanner with O(n3/2) edges that is both a 3-spanner and a (1+ε, 8 log n)-spanner. Furthermore, it is shown that in nO(1/√log n) + O(1/ε) time one can deterministically construct a spanner with O(n3/2) edges which is both a 3-spanner and a (1 + ε, 4)-spanner. This algorithm can be transformed into a Las Vegas randomized algorithm with guarantees on the stretch and time, running in O(ε-1 + log n) expected time.