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
Discrete Mathematics - Topics on domination
Locality in distributed graph algorithms
SIAM Journal on Computing
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Linear-time computability of combinatorial problems on series-parallel graphs
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Constant-time distributed dominating set approximation
Distributed Computing
Distributed almost exact approximations for minor-closed families
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
What can be approximated locally?: case study: dominating sets in planar graphs
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
A log-star distributed maximal independent set algorithm for growth-bounded graphs
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Fast Distributed Approximations in Planar Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Leveraging Linial's Locality Limit
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Approximation hardness of dominating set problems in bounded degree graphs
Information and Computation
Distributed approximation algorithms for weighted problems in minor-closed families
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Distributed graph coloring in a few rounds
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
The south zone: distributed algorithms for alliances
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
ACM Computing Surveys (CSUR)
Constant-factor approximation of the domination number in sparse graphs
European Journal of Combinatorics
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Since in general it is NP-hard to solve the minimum dominating set problem even approximatively, a lot of work has been dedicated to central and distributed approximation algorithms on restricted graph classes. In this paper, we compromise between generality and efficiency by considering the problem on graphs of small arboricity a. These family includes, but is not limited to, graphs excluding fixed minors, such as planar graphs, graphs of (locally) bounded treewidth, or bounded genus. We give two viable distributed algorithms. Our first algorithm employs a forest decomposition, achieving a factor O(a2) approximation in randomized time O(log n). This algorithm can be transformed into a deterministic central routine computing a linear-time constant approximation on a graph of bounded arboricity, without a priori knowledge on a. The second algorithm exhibits an approximation ratio of O(alog Δ), where Δ is the maximum degree, but in turn is uniform and deterministic, and terminates after O(log Δ) rounds. A simple modification offers a trade-off between running time and approximation ratio, that is, for any parameter α ≥ 2, we can obtain an O(aα logα Δ)-approximation within O(logα Δ) rounds.