On Algorithms for the Minimum Link Disjoint Paths Problem

Abstract

Nowadays, the development of robots has created problems whose solution should be found. One of these problems is the search for disjoint paths on polygons with a minimum number of links. The article describes cases when there are several sources and targets at the polygon. The special cases of 2×2 and 3×3 links are considered. The intersection solution in the case of 2×2 is achieved by minimizing the sum of the Euclidean link lengths. If the paths with minimal Euclidean distances intersect, then there is no solution, otherwise solution exists. This method can be extended to the 2×N case. The 3×3 case is solved using an hourglass model. First and third links are taut-string links. The middle link is selected within the side walls of the hourglass. For the case of M×N links, a heuristic algorithm for finding disjoint paths is given. The article also describes an algorithm for constructing forbidden regions that are used in each case.