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
On sparse spanners of weighted graphs
Discrete & Computational Geometry
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
An On-Line Edge-Deletion Problem
Journal of the ACM (JACM)
Approximate distance oracles for unweighted graphs in Õ (n2) time
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Algorithms
Journal of the ACM (JACM)
A simple and linear time randomized algorithm for computing sparse spanners in weighted graphs
Random Structures & 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
Small stretch spanners on dynamic graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Fully dynamic geometric spanners
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Fully dynamic algorithm for graph spanners with poly-logarithmic update time
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Distributed algorithms for ultrasparse spanners and linear size skeletons
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Small stretch (α,β)-spanners in the streaming model
Theoretical Computer Science
Small stretch spanners in the streaming model: new algorithms and experiments
ESA'07 Proceedings of the 15th annual European conference on Algorithms
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)
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
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Let G=(V,E) be an undirected weighted graph on |V|=n vertices and |E|=m edges. For the graph G, A spanner with stretch t is a subgraph (V,ES), Es ⊆ E, such that the distance between any pair of vertices in this subgraph is at most t times the distance between them in the graph G. We present simple and efficient dynamic algorithms for maintaining spanners with essentially optimal (expected) size versus stretch trade-off for any given unweighted graph. The main result is a decremental algorithm that takes expected O(polylog n) time per edge deletion for maintaining a spanner with arbitrary stretch. This algorithm easily leads to a fully dynamic algorithm with sublinear (in n) time per edge insertion or deletion. Quite interestingly, this paper also reports that for stretch at most 6, it is possible to maintain a spanner fully dynamically with expected constant time per update. All these algorithms use simple randomization techniques on the top of an existing static algorithm [6] for computing spanners, and achieve drastic improvement over the previous best deterministic dynamic algorithms for spanners.