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Bounded-degree spanning tree problems: models and new algorithms

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Abstract

Given a connected graph G, a vertex v of G is said to be a branch vertex if its degree is greater than 2. We consider two problems arising in the context of optical networks:

  1. (i)

    Finding a spanning tree of G with the minimum number of branch vertices and

  2. (ii)

    Finding a spanning tree of G such that the degree sum of the branch vertices is minimized.

For these NP-hard problems, heuristics, that give good quality solutions, do not exist in the literature. In this paper we analyze the relation between the problems, provide a single commodity flow formulation to solve the problems by means of a solver and develop different heuristic strategies to compute feasible solutions that are compared with the exact ones. Our extensive computational results show the algorithms to be very fast and effective.

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Authors and Affiliations

  1. Dipartimento di Matematica ed Informatica, Università di Salerno, Via Ponte Don Melillo, 84084, Fisciano (SA), Italy

    R. Cerulli & M. Gentili

  2. Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli studi di Roma “La Sapienza”, P. le Aldo Moro 5, 00185, Rome (RM), Italy

    A. Iossa

Authors
  1. R. Cerulli
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  2. M. Gentili
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  3. A. Iossa
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Correspondence to M. Gentili.

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Cerulli, R., Gentili, M. & Iossa, A. Bounded-degree spanning tree problems: models and new algorithms. Comput Optim Appl 42, 353–370 (2009). https://doi.org/10.1007/s10589-007-9120-2

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  • DOI: https://doi.org/10.1007/s10589-007-9120-2

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