On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs

We consider the problem of computing an optimal range assignment in a wireless network which allows a specified source station to perform a broadcast 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 a...

• Type: Conference
• Year: 2001
• Where: STACS
• Authors: Andrea E. F. Clementi, Pierluigi Crescenzi, Paolo Penna, Gianluca Rossi, Paola Vocca
• Keywords: Range Assignment, Source Node, STACS 2001, Theoretical Computer Science, Wireless Networks