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We study the probabilistic properties of reliable networks of minimum costs in d-dimensional Euclidean space, with reliability in terms of k-edge-connectivity in graphs. We show that this problem fits into Yukich's framework for Euclidean functionals for arbitrary k, dimension d and distant-power gradient p with p < d. With this framework, several theorems on convergence and concentration of the value of optimal solutions follow.These results are then extended to optimal k-edge-connected power assignment graphs, where we assign transmit power to nodes, and two nodes are connected if they both have sufficient transmit power. This variant models wireless networks.Finally, we devise a partitioning heuristic to find approximate solutions quickly, and we analyze its performance in the framework of smoothed analysis.

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Tree based heuristics for the preemptive asymmetric stacker crane problem

Quilliot

Lacroix

Toussaint

et al. 2010

Electronic Notes in Discrete Mathematics

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In this paper, we deal with the preemptive asymmetric stacker crane problem in an heuristic way. We first present some theoretical results which allow us to turn this problem into a specific tree design problem. We next derive from this new representation a simple, efficient local search heuristic, as well as an original LIP model. We conclude by presenting experimental results which aim at both testing the efficiency of our heuristic and at evaluating the impact of the preemption hypothesis

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Cited by 11 publications

References 88 publications

The survivable k-node-connected network design problem: Valid inequalities and Branch-and-Cut

The survivable k-node-connected network design problem: Valid inequalities and Branch-and-Cut

Probabilistic properties of highly connected random geometric graphs

Tree based heuristics for the preemptive asymmetric stacker crane problem

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