Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Approximating the Domatic Number
SIAM Journal on Computing
Global Optimization Using Local Information with Applications to Flow Control
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Energy conservation via domatic partitions
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Decomposition of multiple coverings into many parts
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Decomposition of multiple coverings into more parts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A weakly robust PTAS for minimum clique partition in unit disk graphs
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
DCOSS'10 Proceedings of the 6th IEEE international conference on Distributed Computing in Sensor Systems
Constructing efficient rotating backbones in wireless sensor networks using graph coloring
Computer Communications
Domatic partition in homogeneous wireless sensor networks
Journal of Network and Computer Applications
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We prove a new structural property regarding the "skyline" of uniform radius disks and use this to derive a number of new sequential and distributed approximation algorithms for well-known optimization problems on unit disk graphs (UDGs). Specifically, the paper presents new approximation algorithms for two problems: domatic partition and weighted minimum dominating set (WMDS) on UDGs, both of which are of significant interest to the distributed computing community because of applications to energy conservation in wireless networks. Using the aforementioned skyline property, we derive the first constant-factor approximation algorithm for the domatic partition problem on UDGs. Prior to our work, the best approximation factor for this problem was O (logn ), obtained by simply using the approximation algorithm for general graphs. From the domatic partition algorithm, we derive a new and simpler constant-factor approximation for WMDS on UDGs. Because of "locality" properties that our algorithms possess, both algorithms have relatively simple constant-round distributed implementations in the $\mathcal{LOCAL}$ model, where there is no bound on the message size. In addition, we obtain O (log2 n )-round distributed implementations of these algorithms in the $\mathcal{CONGEST}$ model, where message sizes are bounded above by O (logn ) bits per message.