Discrete Mathematics - Topics on domination
Locality in distributed graph algorithms
SIAM Journal on Computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Approximating the Stretch Factor of Euclidean Graphs
SIAM Journal on Computing
Constructing Plane Spanners of Bounded Degree and Low Weight
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
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
Applications of k-Local MST for Topology Control and Broadcasting in Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Efficient construction of low weight bounded degree planar spanner
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Local 7-coloring for planar subgraphs of unit disk graphs
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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 Construction of Spanners in the 3-D Space
DCOSS '09 Proceedings of the 5th IEEE International Conference on Distributed Computing in Sensor Systems
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We investigate the problem of locally coloring and constructing special spanners of location aware Unit Disk Graphs (UDGs). First we present a local approximation algorithm for the vertex coloring problem in UDGs which uses at most four times as many colors as required by an optimal solution. Then we look at the colorability of spanners of UDGs. In particular we present a local algorithm for constructing a 4-colorable spanner of a unit disk graph. The output consists of the spanner and the 4-coloring. The computed spanner also has the properties that it is planar, the degree of a vertex in the spanner is at most 5 and the angles between two edges are at least *** /3. By enlarging the locality distance (i.e. the size of the neighborhood which a vertex has to explore in order to compute its color) we can ensure the total weight of the spanner to be arbitrarily close to the weight of a minimum spanning tree. We prove that a local algorithm cannot compute a bipartite spanner of a unit disk graph and therefore our algorithm needs at most one color more than any local algorithm for the task requires. Moreover, we prove that there is no local algorithm for 3-coloring UDGs or spanners of UDGs, even if the 3-colorability of the graph (or the spanner respectively) is guaranteed in advance.