Structural complexity 1
Bipartite graphs and their applications
Bipartite graphs and their applications
The Travelling Salesman and the Pq-Tree
Mathematics of Operations Research
Exponential neighbourhood local search for the traveling salesman problem
Computers and Operations Research - Special issue on the traveling salesman problem
Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number
Discrete Applied Mathematics
Domination analysis of some heuristics for the traveling salesman problem
Discrete Applied Mathematics
Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study
INFORMS Journal on Computing
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
TSP tour domination and Hamilton cycle decompositions of regular digraphs
Operations Research Letters
Further Extension of the TSP Assign Neighborhood
Journal of Heuristics
| Hi-index | 0.04 |
We consider the Asymmetric Traveling Salesman Problem (ATSP) and use the definition of neighborhood by Deineko and Woeginger (see Math. Programming 87 (2000) 519-542). Let µ(n) be the maximum cardinality of polynomial time searchable neighborhood for the ATSP on n vertices. Deineko and Woeginger conjectured that µ(n) n - 1)! for any constant β 0 provided P ≠ NP. We prove that µ(n) n - k)! for any fixed integer k ≥ 1 and constant β 0 provided NP ⊈ P/poly, which (like P ≠ NP) is believed to be true. We also give upper bounds for the size of an ATSP neighborhood depending on its search time.