Data di Pubblicazione:
2021
Citazione:
Efficient optimization of the Held–Karp lower bound / G. Righini. - In: OPEN JOURNAL OF MATHEMATICAL OPTIMIZATION.. - ISSN 2777-5860. - 2:(2021), pp. 9.1-9.17. [10.5802/ojmo.11]
Abstract:
Given a weighted undirected graph G = (V,E), the Held–Karp lower bound for the Traveling Salesman Problem (TSP) is
obtained by selecting an arbitrary vertex p 2 V , by computing a minimum cost tree spanning V {p} and adding two
minimum cost edges adjacent to p. In general, different selections of vertex p provide different lower bounds. In this paper
it is shown that the selection of vertex p can be optimized, to obtain the largest possible Held–Karp lower bound, with
the same worst-case computational time complexity required to compute a single minimum spanning tree. Although
motivated by the optimization of the Held–Karp lower bound for the TSP, the algorithm solves a more general problem,
allowing for the efficient pre-computation of alternative minimum spanning trees in weighted graphs where any vertex can
be deleted.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
traveling salesman problem; minimum spanning tree; Held–Karp lower bound; union-find data-structure;
Elenco autori:
G. Righini
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