Annals of Operations Research

, Volume 156, Issue 1, pp 5–24 | Cite as

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

Article
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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.

Keywords

Hamiltonian completion number Dominating trail set Local search Graph algorithms Line graphs 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di SienaSienaItaly
  2. 2.Dipartimento di Elettrotecnica ed ElettronicaPolitecnico di BariBariItaly

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