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Binary Identification Problems for Weighted Trees

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Algorithms and Data Structures (WADS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6844))

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Abstract

The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a node in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T − e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. Moreover, for the degree 2 case, we significantly improve the straightforward O(n 3) dynamic programming approach, and provide an O(n 2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn.

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Author information

Authors and Affiliations

  1. University of Salerno, Italy

    Ferdinando Cicalese

  2. National Institute of Informatics, Japan

    Tobias Jacobs

  3. PUC – Rio de Janeiro, Brazil

    Eduardo Laber & Caio Valentim

Authors
  1. Ferdinando Cicalese
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  2. Tobias Jacobs
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  3. Eduardo Laber
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  4. Caio Valentim
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Editor information

Editors and Affiliations

  1. School of Computer Science, Parallel Computing and Bioinformatics Laboratory, Carleton University, VISM Building, Room 6210, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Frank Dehne

  2. Department of Computer Science and Engineering, Polytechnic Institute of New York University, 5 MetroTech Center, 11201, New York, NY, USA

    John Iacono

  3. School of Computer Science, Herzberg Laboratories, Carleton University, Herzberg Building, Room 5350, 1125 Colonel By Drive, K1S 5B6, Ottawa, ON, Canada

    Jörg-Rüdiger Sack

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© 2011 Springer-Verlag Berlin Heidelberg

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Cicalese, F., Jacobs, T., Laber, E., Valentim, C. (2011). Binary Identification Problems for Weighted Trees. In: Dehne, F., Iacono, J., Sack, JR. (eds) Algorithms and Data Structures. WADS 2011. Lecture Notes in Computer Science, vol 6844. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22300-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-22300-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22299-3

  • Online ISBN: 978-3-642-22300-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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