Finding the hidden path: time bounds for all-pairs shortest paths
SIAM Journal on Computing
The convex-hull-and-line traveling salesman problem: a solvable case
Information Processing Letters
A New Class of Pyramidally Solvable Symmetric Traveling Salesman Problems
SIAM Journal on Discrete Mathematics
Euclidean TSP between two nested convex obstacles
Information Processing Letters
| Hi-index | 5.23 |
We give an O(n^2m+nm^2+m^2logm) time and O(n^2+m^2) space algorithm for finding the shortest traveling salesman tour through the vertices of two simple polygonal obstacles in the Euclidean plane, where n and m are the number of vertices of the two polygons. By obstacle, we mean that the tour may not cross between the interior and exterior of either polygon. We also consider the problem's extension to higher dimensions, proving that, if PNP, constructing a shortest TSP tour on the vertices of two non-intersecting polytopes is NP-hard if the polytopes are similarly viewed as obstacles.