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On the Topologies of Local Minimum Spanning Trees

  • P. F. Cortese
  • G. Di Battista
  • F. Frati
  • L. Grilli
  • K. A. Lehmann
  • G. Liotta
  • M. Patrignani
  • I. G. Tollis
  • F. Trotta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4235)

Abstract

This paper is devoted to study the combinatorial properties of Local Minimum Spanning Trees (LMSTs), a geometric structure that is attracting increasing research interest in the wireless sensor networks community. Namely, we study which topologies are allowed for a sensor network that uses, for supporting connectivity, a local minimum spanning tree approach. First, we refine the current definition of LMST realizability, focusing on the role of the power of transmission (i.e., of the radius of the covered area). Second, we show simple planar, connected, and triangle-free graphs with maximum degree 3 that cannot be represented as an LMST. Third, we present several families of graphs that can be represented as LMSTs. Then, we show a relationship between planar graphs and their representability as LMSTs based on homeomorphism. Finally, we show that the general problem of determining whether a graph is LMST representable is NP-hard.

Keywords

Planar Graph Minimum Span Tree Outerplanar Graph Hexagonal Grid Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • P. F. Cortese
    • 1
  • G. Di Battista
    • 1
  • F. Frati
    • 1
  • L. Grilli
    • 2
  • K. A. Lehmann
    • 3
  • G. Liotta
    • 2
  • M. Patrignani
    • 1
  • I. G. Tollis
    • 4
  • F. Trotta
    • 2
  1. 1.Dipartimento di Informatica e AutomazioneUniversità Roma TreItaly
  2. 2.Dipartimento di Ingegneria Elettronica e dell’InformazioneUniversità di PerugiaItaly
  3. 3.Wilhelm-Schickard Institut für InformatikUniversity of TübingenGermany
  4. 4.Inst. of Computer ScienceFoundation for Research and Technology Hellas-FORTHGreece

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