A Robust and Fast Algorithm for Computing Exact and Approximate Shortest Visiting Routes

Abstract. Given a simple n-sided polygon in the plane with a boundary partitioned into subchains some of which are convex and colored, we consider the following problem: Which is the shortest route (closed path) contained in the polygon that passes through a given point on the boundary and intersects at least one vertex in each of the colored subchains? We present an optimal algorithm that solves this problem in O(n) time. Previously it was known how to solve the problem optimally when each colored subchain contains one vertex only. Moreover, we show that a solution computed by the algorithm is at most a factor 2+c c times longer than the overall shortest route that intersects the subchains (not just at vertices) if the minimal distance between vertices of different subchains is at least c times the maximal length of an edge of a subchain. Without such a bound its length can be arbitrarily longer. Furthermore, it is known that algorithms for computing such overall shortest routes suï¬...

• Type: Conference
• Year: 2004
• Where: ICCSA
• Authors: Håkan Jonsson
• Keywords: Applied Computing, ICCSA 2004, Overall Shortest Routes, Shortest Routes, Simple N-sided Polygon