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- W3157433688 abstract "We study a primitive vehicle routing-type problem in which a fleet of $n$unit speed robots start from a point within a non-obtuse triangle $Delta$, where $n in {1,2,3}$. 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 $Delta$into 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 $nin {1,2,3}$. These subdivisions are the starting points for our main result, which is to study makespan trade-offs with respect to the size of the fleet. In particular, we define $ R_{n,m} (Delta)= max_{P in Delta} R_n(P)/R_m(P)$, and we prove that, over all non-obtuse triangles $Delta$: (i) $R_{1,3}(Delta)$ ranges from $sqrt{10}$ to $4$, (ii) $R_{2,3}(Delta)$ ranges from $sqrt{2}$ to $2$, and (iii) $R_{1,2}(Delta)$ ranges from $5/2$ to $3$. In every case, we pinpoint the starting points within every triangle $Delta$ that maximize $R_{n,m} (Delta)$, as well as we identify the triangles that determine all $inf_Delta R_{n,m}(Delta)$ and $sup_Delta R_{n,m}(Delta)$ over the set of non-obtuse triangles." @default.
- W3157433688 created "2021-05-10" @default.
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- W3157433688 date "2021-05-03" @default.
- W3157433688 modified "2023-09-23" @default.
- W3157433688 title "Makespan Trade-offs for Visiting Triangle Edges" @default.
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