Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem

We extend the work of Letchford (2000) 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.

• Type: Journal
• Year: 2010
• Where: MOR
• Authors: William J. Cook, Daniel G. Espinoza, Marcos Goycoolea
• Keywords: Inequalities, MOR 2010, Traveling Salesman Problem, Well-known Multiple-handle Constraints