A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximating minimum size weakly-connected dominating sets for clustering mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Topology control and routing in ad hoc networks: a survey
ACM SIGACT News
New Distributed Algorithm for Connected Dominating Set in Wireless Ad Hoc Networks
HICSS '02 Proceedings of the 35th Annual Hawaii International Conference on System Sciences (HICSS'02)-Volume 9 - Volume 9
The number of neighbors needed for connectivity of wireless networks
Wireless Networks
Distributed reformation of core-based group-shared multicast trees in mobile ad hoc networks
Journal of Parallel and Distributed Computing
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
Efficient Power Utilization in Multi-radio Wireless Ad Hoc Networks
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
ADHOC-NOW'07 Proceedings of the 6th international conference on Ad-hoc, mobile and wireless networks
IEEE Transactions on Communications
Fault Tolerant Spanners for General Graphs
SIAM Journal on Computing
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fully dynamic randomized algorithms for graph spanners
ACM Transactions on Algorithms (TALG)
Randomized algorithms and probabilistic analysis in wireless networking
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
Deterministic distributed construction of linear stretch spanners in polylogarithmic time
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Multipath spanners via fault-tolerant spanners
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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Motivated by routing issues in ad hoc networks, we present polylogarithmic-time distributed algorithms for two problems. Given a network, we first show how to compute connected and weakly connected dominating sets whose size is at most O(log@D) times the optimum, @D being the maximum degree of the input network. This is best-possible if NP@?DTIME[n^O^(^l^o^g^l^o^g^n^)] and if the processors are required to run in polynomial-time. We then show how to construct dominating sets that have the above properties, as well as the ''low stretch'' property that any two adjacent nodes in the network have their dominators at a distance of at most O(logn) in the output network. (Given a dominating set S, a dominator of a vertex u is any v@?S such that the distance between u and v is at most one.) We also show our time bounds to be essentially optimal.