Makespan Trade-Offs for Visiting Triangle Edges

نویسندگان

چکیده

We study a primitive vehicle routing-type problem in which fleet of n unit speed robots start from point within non-obtuse triangle $$\Delta $$ , where $$n \in \{1,2,3\}$$ . The goal is to design robots’ trajectories so as visit all edges the with smallest visitation time makespan. begin our by introducing framework for subdividing into regions respect type optimal trajectory that each P admits, pertaining order are visited and how cost minimum makespan $$R_n(P)$$ determined, $$n\in These subdivisions starting points main result, trade-offs size fleet. In particular, we define $$\mathscr {R}_{n,m} (\Delta )= \max _{P \Delta } R_n(P)/R_m(P)$$ prove that, over triangles : (i) {R}_{1,3}(\Delta )$$ ranges $$\sqrt{10}$$ 4, (ii) {R}_{2,3}(\Delta $$\sqrt{2}$$ 2, (iii) {R}_{1,2}(\Delta 5/2 3. every case, pinpoint maximize well identify determine $$\inf _\Delta \mathscr {R}_{n,m}(\Delta $$\sup set triangles.

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ژورنال

عنوان ژورنال: Lecture Notes in Computer Science

سال: 2021

ISSN: ['1611-3349', '0302-9743']

DOI: https://doi.org/10.1007/978-3-030-79987-8_24