Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem

Authors:
William J. Cook;Daniel G. Espinoza;Marcos Goycoolea
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205;Departamento de Ingeniería Industrial, Universidad de Chile, 8370448 Santiago, Chile;School of Business, Universidad Adolfo Ibaòez, 7941169 Santiago, Chile
Venue:
Mathematics of Operations Research
Year:
2010

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Abstract

We extend the work of Letchford [Letchford, A. N. 2000. Separating a superclass of comb inequalities in planar graphs. Math. Oper. Res.25 443--454] by introducing a new class of valid inequalities for the traveling salesman problem, called the generalized domino-parity (GDP) constraints. Just as Letchford's domino-parity constraints generalize comb inequalities, GDP constraints generalize the most well-known multiple-handle constraints, including clique-tree, bipartition, path, and star inequalities. Furthermore, we show that a subset of GDP constraints containing all of the clique-tree inequalities can be separated in polynomial time, provided that the support graph G* is planar, and provided that we bound the number of handles by a fixed constant h.