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Algorithms, graphs, and computers by R Cooke, K L. Lockett, J A Bellman

By R Cooke, K L. Lockett, J A Bellman

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In unit disk graphs, the problem (as well as its connected counterpart) remains N P-hard, but constant approximations become possible. In unit disk graphs and some of its generalizations, the problem even allows for a polynomial time approximation scheme (PTAS) [192, 70, 116], even without geometric representation [303]. In the distributed case, the complexity of computing a good dominating set depends on the model assumptions. In the easiest model - when all nodes know their coordinates - a constant approximation to MDS can be computed with only two rounds of communication!

The oceans are one example. g. for the emergence of hurricanes. However, to explore the oceans with sensor networks, research into underwater communication and sensor design for underwater missions is necessary. In the long run, sensor networks may be of good use in space-related research. For example instead of sending one single sensor system like the Mars Rover to a distant planet, it would perhaps be possible in the future to deploy a sensor network consisting of thousands of nodes. -J. Hof Fig.

Since all nodes within one cell are at most at distance 1 to each other, nodes in each cluster can simply elect one “clusterleader” per cell (for instance the node with the lowest ID). The union of all these leaders covers the entire graph and it is easy to see that it is a constant approximation to the optimal solution: For every cell, the optimal solution places at least one dominator in the cell or in one of the neighboring cells. If nodes do not know their coordinates, the problem becomes more involved.

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