On the complexity of computing minimum energy consumption broadcast subgraphs

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On the complexity of computing minimum energy consumption broadcast subgraphs (2001)

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by Andrea E. F. Clementi , Pilu Crescenzi , Paolo Penna , Gianluca Rossi , Paola Vocca

Venue:	in Symposium on Theoretical Aspects of Computer Science
Citations:	110 - 13 self

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@INPROCEEDINGS{Clementi01onthe,
    author = {Andrea E. F. Clementi and Pilu Crescenzi and Paolo Penna and Gianluca Rossi and Paola Vocca},
    title = {On the complexity of computing minimum energy consumption broadcast subgraphs},
    booktitle = {in Symposium on Theoretical Aspects of Computer Science},
    year = {2001},
    pages = {121--131},
    publisher = {Springer-Verlag}
}

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Abstract

Abstract. 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 constant 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. 1

Keyphrases

minimum energy consumption broadcast subgraphs source node np-hard case polynomial-time approximation algorithm source station minimum energy consumption broadcast subgraph optimal range assignment distance-power gradient minimum cost range assignment main result constant factor broadcast operation geometric space dimension transmission graph special case general combinatorial optimization problem wireless network weighted directed graph negative result

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