Acute Tours in the Plane

11/30/2021

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by   Ahmad Biniaz, et al.

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We confirm the following conjecture of Fekete and Woeginger from 1997: for any sufficiently large even number n, every set of n points in the plane can be connected by a spanning tour (Hamiltonian cycle) consisting of straight-line edges such that the angle between any two consecutive edges is at most π/2. Our proof is constructive and suggests a simple O(nlog n)-time algorithm for finding such a tour. The previous best-known upper bound on the angle is 2π/3, and it is due to Dumitrescu, Pach and Tóth (2009).