The Touring Polygons Problem Revisited

Xuehou TAN  Bo JIANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.5   pp.772-777
Publication Date: 2018/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.772
Type of Manuscript: PAPER
Category: Algorithms and Data Structures
Keyword: 
shortest path,  touring polygons problem,  last step shortest path map,  convex polygons,  

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Summary: 
Given a sequence of k convex polygons in the plane, a start point s, and a target point t, we seek a shortest path that starts at s, visits in order each of the polygons, and ends at t. We revisit this touring polygons problem, which was introduced by Dror et al. (STOC 2003), by describing a simple method to compute the so-called last step shortest path maps, one per polygon. We obtain an O(kn)-time solution to the problem for a sequence of pairwise disjoint convex polygons and an O(k2n)-time solution for possibly intersecting convex polygons, where n is the total number of vertices of all polygons. A major simplification is made on the operation of locating query points in the last step shortest path maps. Our results improve upon the previous time bounds roughly by a factor of log n.