Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Message-optimal connected dominating sets in 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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Fast distributed algorithms for (weakly) connected dominating sets and linear-size skeletons
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Connected Dominating Sets
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Global Optimization Using Local Information with Applications to Flow Control
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Distributed verification of minimum spanning trees
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Distributed approximation of capacitated dominating sets
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
A local algorithm for dominating sets of quasi-unit disk graphs
C3S2E '09 Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering
A new local algorithm for backbone formation in ad hoc networks
Proceedings of the 6th ACM symposium on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
Dynamic virtual backbone management for service discovery in wireless mesh networks
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
Local Algorithms: Self-stabilization on Speed
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Brief announcement: efficient graph algorithms without synchronization
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Rapid randomized pruning for fast greedy distributed algorithms
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Minimum dominating set approximation in graphs of bounded arboricity
DISC'10 Proceedings of the 24th international conference on Distributed computing
Distributed graph coloring in a few rounds
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Structuring unreliable radio networks
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Analysing local algorithms in location-aware quasi-unit-disk graphs
Discrete Applied Mathematics
Algorithms for the minimum weight k-fold (connected) dominating set problem
Journal of Combinatorial Optimization
ACM Computing Surveys (CSUR)
Lower bounds for local approximation
Journal of the ACM (JACM)
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Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree Δ, our algorithm computes a dominating set of expected size O(kΔ2/k log (Δ)|DSOPT|) in O (K2) rounds. Each node has to send O(k2 Δ) messages of size O(log Δ). This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.