Reoptimizing the Strengthened Metric TSP on Multiple Edge Weight Modifications

  • Annalisa D’Andrea
  • Guido Proietti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7276)


We consider the following (re)optimization problem: Given a minimum-cost Hamiltonian cycle of a complete non-negatively real weighted graph G = (V,E,c) obeying the strengthened triangle inequality (i.e., for some strength factor \(\frac{1}{2} \leq \beta <1\), we have that ∀ x,y,z ∈ V, c(x,y) ≤ β(c(x,z) + c(y,z))), and given a set of k edge weight modifications producing a new weighted graph still obeying the strengthened triangle inequality, find a minimum-cost Hamiltonian cycle of the modified graph. This problem is known to be NP-hard already for a single edge weight modification. However, in this case, if both the input and the modified graph obey the strengthened triangle inequality and the respective strength factors are fixed (i.e., independent of |V|), then it has been shown that the problem admits a PTAS (which just consists of either returning the old optimal cycle, or instead computing — for finitely many inputs — a new optimal solution from scratch, depending on the required accuracy in the approximation). In this paper we first extend the analysis of the PTAS to show its applicability for all k = O(1), and then we provide a large set of experiments showing that, in most practical circumstances, altering (uniformly at random) even several edge weights does not affect the goodness of the old optimal solution.


Triangle Inequality Edge Weight Travel Salesman Problem Travel Salesman Problem Steiner Tree 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Annalisa D’Andrea
    • 1
  • Guido Proietti
    • 1
    • 2
  1. 1.Dipartimento di InformaticaUniversity of L’AquilaItaly
  2. 2.Istituto di Analisi dei Sistemi ed Informatica, CNRRomeItaly

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