On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs

  • Andrea E. F. Clementi
  • Pilu Crescenzi
  • Paolo Penna
  • Gianluca Rossi
  • Paola Vocca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)


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.


Span Tree Source Node Minimum Span Tree Minimum Energy Consumption Weighted Directed Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Andrea E. F. Clementi
    • 1
  • Pilu Crescenzi
    • 2
  • Paolo Penna
    • 1
  • Gianluca Rossi
    • 2
  • Paola Vocca
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly

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