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Destruction of Very Simple Trees

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Abstract

We consider the total cost of cutting down a random rooted tree chosen from a family of so-called very simple trees (which include ordered trees, d-ary trees, and Cayley trees); these form a subfamily of simply generated trees. At each stage of the process an edge is chosen at random from the tree and cut, separating the tree into two components. In the one-sided variant of the process the component not containing the root is discarded, whereas in the two-sided variant both components are kept. The process ends when no edges remain for cutting. The cost of cutting an edge from a tree of size n is assumed to be nα. Using singularity analysis and the method of moments, we derive the limiting distribution of the total cost accrued in both variants of this process. A salient feature of the limiting distributions obtained (after normalizing in a family-specific manner) is that they only depend on α.

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Authors and Affiliations

  1. Applied Mathematics and Statistics, The Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218-2682, USA

    James Allen Fill

  2. Computer Science, California Institute of Technology, MC 256-80, 1200 E. California Blvd., Pasadena, CA 91125, USA

    Nevin Kapur

  3. Institut fur Diskrete Mathematik und Geometrie, Technische Universitat Wien, Wiedner Hauptstrasse 8-10/104, A-1040, Wien, Austria

    Alois Panholzer

Authors
  1. James Allen Fill
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  2. Nevin Kapur
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  3. Alois Panholzer
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Correspondence to James Allen Fill, Nevin Kapur or Alois Panholzer.

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Fill, J., Kapur, N. & Panholzer, A. Destruction of Very Simple Trees. Algorithmica 46, 345–366 (2006). https://doi.org/10.1007/s00453-006-0100-1

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  • DOI: https://doi.org/10.1007/s00453-006-0100-1

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