Differential approximation results for the traveling salesman and related problems
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Travelling Salesman and the PQ-Tree
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Efficient algorithms for the double traveling salesman problem with multiple stacks
Computers and Operations Research
The uncapacitated asymmetric traveling salesman problem with multiple stacks
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Differential approximation of the multiple stacks TSP
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
A Branch-and-Cut Algorithm for the Double Traveling Salesman Problem with Multiple Stacks
INFORMS Journal on Computing
The traveling purchaser problem, with multiple stacks and deliveries: A branch-and-cut approach
Computers and Operations Research
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Given a universal constant k , the multiple Stack Travelling Salesman Problem (k STSP in short) consists in finding a pickup tour T 1 and a delivery tour T 2 of n items on two distinct graphs. The pickup tour successively stores the items at the top of k containers, whereas the delivery tour successively picks the items at the current top of the containers: thus, the couple of tours are subject to LIFO ("Last In First Out" ) constraints. This paper aims at finely characterizing the complexity of k STSP in regards to the complexity of TSP. First, we exhibit tractable sub-problems: on the one hand, given two tours T 1 and T 2, deciding whether T 1 and T 2 are compatible can be done within polynomial time; on the other hand, given an ordering of the n items into the k containers, the optimal tours can also be computed within polynomial time. Note that, to the best of our knowledge, the only family of combinatorial precedence constraints for which constrained TSP has been proven to be in P is the one of PQ-trees, [2]. Finally, in a more prospective way and having in mind the design of approximation algorithms, we study the relationship between optimal value of different TSP problems and the optimal value of k STSP.