Problems and Results

Assume that a point-robot moves in straight-line paths inside a polygonal region P. Every time it has to change its direction of the path, it stops and rotates until it directs itself to the new direction. In the process, it makes several turns before reaching its destination. If straight line motions are ‘cheap’ but rotations are ‘expensive’, minimizing the number of turns reduces the cost of the motion although it may increase the length of the path. This motivates the study of link paths inside a polygonal region P. For more details on applications of such paths, see the review article of Maheshwari et al. [253].

A link path between two points s and t of a polygon P (with or without holes) is a path inside P that connects s and t by a chain of line segments (called links). A minimum link path between s and t is a link path connecting s and t that has the minimum number of links (see Figure 7.1). Observe that there may be several link paths between s and t with the minimum number of links. The link distance between any two points of P is the number of links in the minimum link path between them.

The problem of computing the minimum link path between any two points inside a simple polygon were first studied by ElGindy [126] and Suri [318].