Servicing Timed Requests on a Line
A. Gkikas, T. Radzik

TL;DR
This paper addresses an off-line optimization problem where multiple robots service weighted requests on a line, proposing a recursive algorithm that improves computational efficiency for fixed numbers of robots.
Contribution
It introduces a recursive algorithm with improved time complexity for solving the robot scheduling problem with arbitrary request weights, especially when the number of robots is fixed.
Findings
Developed a recursive $O(k^{2k}n \\log^{2k} n)$-time algorithm.
Improved previous algorithms' running times for fixed $k$.
Identified properties of the problem that could lead to more efficient solutions.
Abstract
We consider an off-line optimisation problem where robots must service requests on a single line. A request has weight and takes place at time at location on the line. A robot can service a request and collect the weight , if it is present at at time . The objective is to find robot-schedules that maximize the total weight. The optimisation problem is motivated by a robotics application [Asahiro et al. Discrete Applied Mathematics, 2006] and can be modeled as a minimum cost flow problem with unit capacities in a flow network . Consequently, we ask for a collection of node-disjoint paths from the source to the sink in , with minimum total weight. It was shown in [Asahiro et al. Discrete Applied Mathematics, 2006] that the flow network can be implicitly represented by points on the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOptimization and Search Problems · Vehicle Routing Optimization Methods · Robotic Path Planning Algorithms
