IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Regular Section
The Touring Polygons Problem Revisited
Xuehou TANBo JIANG
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2018 Volume E101.A Issue 5 Pages 772-777

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Abstract

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.

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© 2018 The Institute of Electronics, Information and Communication Engineers
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