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Local search algorithms for finding the Hamiltonian completion number of line graphs

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  • Paolo Detti
  • Carlo Meloni
  • Marco Pranzo

Abstract

Given a graph G=(V,E), the Hamiltonian completion number of G, HCN(G), is the minimum number of edges to be added to G to make it Hamiltonian. This problem is known to be $\mathcal{NP}$ -hard even when G is a line graph. In this paper, local search algorithms for finding HCN(G) when G is a line graph are proposed. The adopted approach is mainly based on finding a set of edge-disjoint trails that dominates all the edges of the root graph of G. Extensive computational experiments conducted on a wide set of instances allow to point out the behavior of the proposed algorithms with respect to both the quality of the solutions and the computation time. Copyright Springer Science+Business Media, LLC 2007

Suggested Citation

  • Paolo Detti & Carlo Meloni & Marco Pranzo, 2007. "Local search algorithms for finding the Hamiltonian completion number of line graphs," Annals of Operations Research, Springer, vol. 156(1), pages 5-24, December.
    • Handle: RePEc:spr:annopr:v:156:y:2007:i:1:p:5-24:10.1007/s10479-007-0231-z
    DOI: 10.1007/s10479-007-0231-z
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    References listed on IDEAS

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    1. A. Agnetis & P. Detti & C. Meloni & D. Pacciarelli, 2001. "Set-Up Coordination between Two Stages of a Supply Chain," Annals of Operations Research, Springer, vol. 107(1), pages 15-32, October.
    2. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    3. Egon Balas & Alkis Vazacopoulos, 1998. "Guided Local Search with Shifting Bottleneck for Job Shop Scheduling," Management Science, INFORMS, vol. 44(2), pages 262-275, February.
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    Cited by:

    1. Liao, Ching-Jong & Shyu, Cian-Ci & Tseng, Chao-Tang, 2009. "A least flexibility first heuristic to coordinate setups in a two- or three-stage supply chain," International Journal of Production Economics, Elsevier, vol. 117(1), pages 127-135, January.
    2. Jorik Jooken & Pieter Leyman & Patrick Causmaecker, 2020. "A multi-start local search algorithm for the Hamiltonian completion problem on undirected graphs," Journal of Heuristics, Springer, vol. 26(5), pages 743-769, October.

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