Counting feasible solutions of the traveling salesman problem with pickups and deliveries is #P-complete

Authors:
Gerardo Berbeglia;Geňa Hahn
Affiliations:
Canada Research Chair in Distribution Management, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montreal, H3T 2A7, Canada;Département d'informatique et de recherche opérationnelle, Université de Montréal, C.P. 6128, succursale Centre-ville, Montreal, H3C 3J7, Canada
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

Deciding whether or not a feasible solution to the Traveling Salesman Problem with Pickups and Deliveries (TSPPD) exists is polynomially solvable. We prove that counting the number of feasible solutions of the TSPPD is hard by showing that the problem is #P-complete.