Approximate shortest path algorithms for sequences of pairwise disjoint simple polygons

Assume that two points p and q are given and a finite ordered set of simple polygons, all in the same plane; the basic version of a touring-a-sequence-of-polygons problem (TPP) is to find a shortest path such that it starts at p, then visits these polygons in the given order, and ends at q. This paper describes four approximation algorithms for unconstrained versions of problems defined by touring an ordered set of polygons. It contributes to an approximate and partial answer to the previously open problem "What is the complexity of the touringpolygons problem for pairwise disjoint, simple and not necessarily convex polygons?" by providing ()O(n) approximation algorithms for solving this problem, either for given start and end points p and q, or with allowing to have those variable, where n is the total number of vertices of the given k simple and pairwise disjoint polygons; () defines the numerical accuracy in dependency of a selected > 0.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Xiuxia Pan, Fajie Li, Reinhard Klette
• Keywords: Approximation Algorithms, CCCG 2010, Computational Geometry, Finite Ordered Set, Simple Polygons