Convex blocking and partial orders on the plane

8 years 3 months ago
Convex blocking and partial orders on the plane
Let C = {c1, . . . , cn} be a collection of disjoint closed bounded convex sets in the plane. Suppose that one of them, say c1, represents a valuable object we want to uncover, and we are allowed to pick a direction α ∈ [0, 2π) along which we can translate (remove) the elements of C, one at a time, while avoiding collisions. We study the problem of finding a direction α0 such that the number of elements that have to be removed along α0 before we can remove c1 is minimized. We prove that if we have the sorted set D of directions defined by the tangents between pairs of elements of C, we can find α0 in O(n2 ) time. We also discuss the problem of sorting D in o(n2 log n) time.
José Miguel Díaz-Báñez
Added 31 Mar 2016
Updated 31 Mar 2016
Type Journal
Year 2016
Authors José Miguel Díaz-Báñez, Marco A. Heredia, Canek Peláez, Joan Antoni Sellarès, Jorge Urrutia, Inmaculada Ventura
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