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Near-optimal bounded-degree spanning trees

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Abstract

Random costsC(i, j) are assigned to the arcs of a complete directed graph onn labeled vertices. Given the cost matrixC n =(C(i, j)), letT* k =T* k (C n ) be the spanning tree that has minimum cost among spanning trees with in-degree less than or equal tok. Since it is NP-hard to findT* k , we instead consider an efficient algorithm that finds a near-optimal spanning treeT a k . If the edge costs are independent, with a common exponential(I) distribution, then, asn → ∞,

$$E(Cost(T_k^a {\text{)) = }}E(Cost(T_k^* {\text{)) + }}o\left( 1 \right).$$

Upper and lower bounds forE(Cost(T* k )) are also obtained fork≥2.

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Authors and Affiliations

  1. Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, Scotland

    J. C. Hansen

  2. Department of Mathematics and Computer Science, Drexel University, 19104, Philadelphia, PA, USA

    E. Schmutz

Authors
  1. J. C. Hansen
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  2. E. Schmutz
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Additional information

Communicated by H. Prodinger and W. Szpankowski.

Online publication October 6, 2000.

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Hansen, J.C., Schmutz, E. Near-optimal bounded-degree spanning trees. Algorithmica 29, 148–180 (2001). https://doi.org/10.1007/BF02679617

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  • DOI: https://doi.org/10.1007/BF02679617

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