
CramerCastillon on a Triangle's Incircle and Excircles
The CramerCastillon problem (CCP) consists in finding one or more polyg...
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Obnoxious facility location: the case of weighted demand points
The problem considered in this paper is the weighted obnoxious facility ...
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Largest and Smallest Area Triangles on Imprecise Points
Assume we are given a set of parallel line segments in the plane, and we...
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Largest and Smallest Area Triangles on a Given Set of Imprecise Points
In this paper we study the following problem: we are given a set of impr...
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Monochromatic Triangles, Triangle Listing and APSP
One of the main hypotheses in finegrained complexity is that AllPairs ...
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Tukey Depth Histograms
The Tukey depth of a flat with respect to a point set is a concept that ...
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Enforcing Interpretability and its Statistical Impacts: Tradeoffs between Accuracy and Interpretability
To date, there has been no formal study of the statistical cost of inter...
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Makespan Tradeoffs for Visiting Triangle Edges
We study a primitive vehicle routingtype problem in which a fleet of nunit speed robots start from a point within a nonobtuse triangle Δ, where n ∈{1,2,3}. The goal is to design robots' trajectories so as to visit all edges of the triangle with the smallest visitation time makespan. We begin our study by introducing a framework for subdividing Δinto regions with respect to the type of optimal trajectory that each point P admits, pertaining to the order that edges are visited and to how the cost of the minimum makespan R_n(P) is determined, for n∈{1,2,3}. These subdivisions are the starting points for our main result, which is to study makespan tradeoffs with respect to the size of the fleet. In particular, we define R_n,m (Δ)= max_P ∈Δ R_n(P)/R_m(P), and we prove that, over all nonobtuse triangles Δ: (i) R_1,3(Δ) ranges from √(10) to 4, (ii) R_2,3(Δ) ranges from √(2) to 2, and (iii) R_1,2(Δ) ranges from 5/2 to 3. In every case, we pinpoint the starting points within every triangle Δ that maximize R_n,m (Δ), as well as we identify the triangles that determine all inf_Δ R_n,m(Δ) and sup_Δ R_n,m(Δ) over the set of nonobtuse triangles.
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