Abstract
We consider the problem of computing an optimal range assignment in a wireless network which allows a specified source station to perform a broad- cast operation. In particular, we consider this problem as a special case of the following more general combinatorial optimization problem, called Minimum Energy Consumption Broadcast Subgraph (in short, MECBS): Given a weighted directed graph and a specified source node, find a minimum cost range assignment to the nodes, whose corresponding transmission graph contains a spanning tree rooted at the source node. We first prove that MECBS is not approximable within a sub-logarithmic factor (unless P=NP).We then consider the restriction of MECBS to wireless networks and we prove several positive and negative results, depending on the geometric space dimension and on the distance-power gradient. The main result is a polynomial-time approximation algorithm for the NP-hard case in which both the dimension and the gradient are equal to 2: This algorithm can be generalized to the case in which the gradient is greater than or equal to the dimension.
Research partially supported by ItalianMURST project “Algoritmi per Grandi Insiemi di Dati: Scienza ed Ingegneria”.
Part of this work has been done while visiting INRIA Sophia Antipolis (MASCOTTE Project).
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Clementi, A.E.F., Crescenzi, P., Penna, P., Rossi, G., Vocca, P. (2001). On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_11
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