A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Linear algorithm for domatic number problem on interval graphs
Information Processing Letters
On the parallel complexity of computing a maximal independent set in a hypergraph
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Information Processing Letters
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
Parallel search for maximal independence given minimal dependence
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Approximating the Domatic Number
SIAM Journal on Computing
Efficient NC algorithms for set cover with applications to learning and geometry
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Fast deterministic distributed maximal independent set computation on growth-bounded graphs
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Monitoring schedules for randomly deployed sensor networks
Proceedings of the fifth international workshop on Foundations of mobile computing
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Given n sensors and m targets, a monitoring schedule is a partition of the sensor set such that each subset of the partition can monitor all the targets. Monitoring schedules are used for maximizing the time all the targets are monitored when there is no possibility of replacing the batteries of the sensors. Each subset of the partition is used for one unit of time, and thus the goal is to maximize the number of subsets in the partition. We make the assumption that any two sensors for which there is a target both can monitor can communicate in one hop. The Monitoring Schedule problem is closely related to the domatic number in graphs and from previous work one can obtain a logarithmic approximation with one round of communication. We consider the special case when the targets are on a curve (such as a road) and each sensor can monitor an interval of the curve. For this case an optimum schedule can be computed in centralized manner. However, in the worst case a localized algorithm requires a linear number of communication rounds to compute a solution which is better than a 2-approximation. We present a (2+@e)-approximate randomized localized algorithm with polylogarithmic number of communication rounds.