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

Discrete Applied Mathematics

Volumn 157, Issue 11, 2009, Pages 2541-2547

  Berbeglia, Gerardo ^a   Hahn, Geňa ^b  

^a HEC MONTRÉAL   (Canada)

^b UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

P complete; Complexity; Counting solutions; Traveling salesman problem with pickups and deliveries

Indexed keywords

# P-COMPLETE; COMPLEXITY; COUNTING SOLUTIONS; FEASIBLE SOLUTIONS;

PROBLEM SOLVING;

TRAVELING SALESMAN PROBLEM;

EID: 67349158071     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2009.03.003     Document Type: Article

References (15)

1. Aminu U.F., and Eglese R.W. A constraint programming approach to the Chinese postman problem with time windows. Computers and Operations Research 33 (2006) 3423-3431
2. Bourgeois M., Laporte G., and Semet F. Heuristics for the black and white traveling salesman problem. Computers and Operations Research 30 (2003) 75-85
3. J.-F. Cordeau, M. Iori, G. Laporte, J.J. Salazar González, A branch-and-cut algorithm for the pickup and delivery traveling salesman problem with LIFO loading, Networks (2008) (in press)
4. Graham R.L., Knuth D.E., and Patashnik O. Concrete Mathematics (1989), Addison-Wesley, New York
5. Healy P., and Moll R. A new extension of local search applied to the dial-a-ride problem. Transportation Science 14 (1980) 130-154
6. Hoffman K., and Kunze R. Linear Algebra (1971), Prentice Hall, NJ
7. Jerrum M. Counting, Sampling and Integrating: Algorithms and Complexity. Lectures in Mathematics - ETH Zürich (2003), Birkhäuser Verlag, Basel
8. Mak V., and Boland N. Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs. Discrete Applied Mathematics 155 (2007) 2093-2110
9. Mosheiov G. The traveling salesman problem with pick-up and delivery. European Journal of Operational Research 79 (1994) 299-310
10. Papadimitriou C.H. Computational Complexity (1995), Addison-Wesley, Reading, MA
11. G. Pesant, Counting solutions of CSPs: A Structural Approach, International Joint Conferences on Artificial Intelligence, IJCAI-05: 2005, pp. 260-265
12. Ruland K.S., and Rodin E.Y. The pickup and delivery problem: Faces and branch-and-cut algorithm. Computers and Mathematics with Applications 33 (1997) 1-13
13. L. Trevisan, Computational Theory, Lecture 6, available at http://www.cs.berkeley.edu/~luca/cs278-08/lecture06.pdf, 2008
14. Valiant L.G. The complexity of computing the permanent. Theoretical Computer Science 8 (1979) 189-201
15. Valiant L.G. The complexity of enumeration and reliability problems. SIAM Journal of Computing 8 (1979) 410-421