Theory of Computing Systems

, Volume 42, Issue 3, pp 289–305

# Grasp and Delivery for Moving Objects on Broken Lines

• Yuichi Asahiro
• Eiji Miyano
• Shinichi Shimoirisa
Article

## Abstract

This paper studies the following variant of the Vehicle Routing Problem that we call the Grasp and Delivery for Moving Objects (GDMO) problem, motivated by robot navigation: The input to the problem consists of n products, each of which moves on a predefined path with a fixed constant speed, and a robot arm of capacity one. In each round, the robot arm grasps one product and then delivers it to the depot. The goal of the problem is to find a collection of tours such that the robot arm grasps and delivers as many products as possible. In this paper we prove the following results: (i) If the products move on broken lines with at least one bend, then the GDMO is MAXSNP-hard, and (ii) it can be approximated with ratio 2. However, (iii) if we impose the “straight line without bend” restriction on the motion of every product, then the GDMO becomes tractable.

## Keywords

Moving objects Grasp and delivery Approximation algorithm MAXSNP-hardness

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## Authors and Affiliations

• Yuichi Asahiro
• 1
Email author
• Eiji Miyano
• 2
• Shinichi Shimoirisa
• 2
1. 1.Department of Social Information SystemsKyushu Sangyo UniversityFukuokaJapan
2. 2.Department of Systems Innovation and InformaticsKyushu Institute of TechnologyFukuokaJapan