A simple parallel algorithm for the maximal independent set problem
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
On approximating the minimum independent dominating set
Information Processing Letters
Discrete Mathematics - Topics on domination
Locality in distributed graph algorithms
SIAM Journal on Computing
SIAM Journal on Computing
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Unit disk graph recognition is NP-hard
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Message-optimal connected dominating sets in mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
An efficient distributed algorithm for constructing small dominating sets
Distributed Computing - Special issue: Selected papers from PODC '01
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Proceedings of the 2004 joint workshop on Foundations of mobile computing
On the locality of bounded growth
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Local approximation schemes for ad hoc and sensor networks
DIALM-POMC '05 Proceedings of the 2005 joint workshop on Foundations of mobile 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
A simple improved distributed algorithm for minimum CDS in unit disk graphs
ACM Transactions on Sensor Networks (TOSN)
Broadcasting in geometric radio networks
Journal of Discrete Algorithms
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
A PTAS for the minimum dominating set problem in unit disk graphs
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Local construction of planar spanners in unit disk graphs with irregular transmission ranges
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
DCOSS '08 Proceedings of the 4th IEEE international conference on Distributed Computing in Sensor Systems
Local PTAS for Dominating and Connected Dominating Set in Location Aware Unit Disk Graphs
Approximation and Online Algorithms
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
Deterministic dominating set construction in networks with bounded degree
ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
Analysing local algorithms in location-aware quasi-unit-disk graphs
Discrete Applied Mathematics
ACM Computing Surveys (CSUR)
Secure local algorithm for establishing a virtual backbone in 3D ad hoc network
International Journal of Networking and Virtual Organisations
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Many protocols in ad-hoc networks use dominating and connected dominating sets, for example for broadcasting and routing. For large ad hoc networks the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant number of hops from it. In this paper we use the location awareness of the network, i.e. the knowledge of position of nodes in the plane to provide local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + Ɛ the optimal, for any arbitrarily small Ɛ 0. These are to our knowledge the first local algorithms whose time complexities and approximation bounds are independent of the size of the network.