Construction Heuristics and Domination Analysis for the Asymmetric TSP
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
A survey of very large-scale neighborhood search techniques
Discrete Applied Mathematics
| Hi-index | 0.00 |
An exponential neighbourhood for the traveling salesman problem (TSP) is a set of tours, which grows exponentially in the input size. An exponential neighbourhood is polynomial time searchable if we can find the best among the exponential number of tours in polynomial time. Deineko and Woeginger asked if there exists polynomial time searchable neighbourhoods of size at least $(q n)!$, for some $q q 1$. Deineko and Woeginger proved (indirectly) that if $P\not=NP$ then no algorithm for searching a neighbourhood of size $(q n) !$ can run faster then $O(n^{1+q})$.