Abstract
We consider the following variant of the Vehicle Routing Problem that we call the Pickup and Delivery for Moving Objects (PDMO) 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 and delivers one product to its original position. 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 PDMO is MAXSNP-hard, and (ii) it can be approximated with ratio two. However, (iii) if we impose the “straight line without bend” restriction on the motion of every product, then the PDMO becomes tractable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Toth, P., Vigo, D.: An overview of vehicle routing problems. In: Tosh, P., Vigo, D. (eds.) The Vehicle Routing Problem. SIAM, Philadelphia (2001)
Bansal, N., Blum, A., Chawla, S., Meyerson, A.: Approximation algorithms for deadline-TSP and vehicle routing with time-windows. In: Proc. ACM Symposium on Theory of Computing, pp. 166–174 (2004)
Blum, A., Chawla, S., Karger, D., Lane, T., Meyerson, A., Minkoff, M.: Approximation algorithms for orienteering and discounted-reward TSP. In: Proc. IEEE Symposium on Foundations of Computer Science, pp. 46–55 (2003)
Desrochers, M., Desrosiers, J., Solomon, M.M.: A new optimization algorithm for the vehicle routing problem with time windows. Operations Research 40, 342–354 (1992)
Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.): The traveling salesman problem. Wiley, Chichester (1985)
Chalasani, P., Motwani, R., Rao, A.: Approximation algorithms for robot grasp and delivery. In: Proc. International Workshop on Algorithmic Foundations of Robotics, pp. 347–362 (1996)
Helvig, C.S., Robins, G., Zelikovsky, A.: Moving target TSP and related problems. In: Proc. European Symposium on Algorithms, pp. 453–464 (1998)
Hammar, M., Nilsson, B.J.: Approximation results for kinetic variants of TSP. In: Proc. International Colloquium on Automata, Languages and Programming, pp. 392–401 (1999)
Asahiro, Y., Horiyama, T., Makino, K., Ono, H., Sakuma, T., Yamashita, M.: How to collect balls moving in the Euclidean plane. Electronic Notes in Theoretical Computer Science 91, 229–245 (2004)
Asahiro, Y., Miyano, E., Shimoirisa, S.: K-collect tours for moving objects with release times and deadlines. In: To appear in Proc. Systemics, Cybernetics and Informatics (2005)
Lenstra, J.K., Rinnooy Kan, A.H.G., Brucker, P.: Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343–362 (1977)
Moore, J.M.: An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science 15, 102–109 (1968)
Spieksma, F.C.R.: On the approximability of an interval scheduling problem. Journal of Scheduling 2, 215–227 (1999)
Karger, D., Stein, C., Wein, J.: Scheduling algorithms. In: Atallah, M.J. (ed.) Handbook of Algorithms and Theory of Computation. CRC Press, Boca Raton (1997)
Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Approximating the throughput of multiple machines under real-time scheduling. SIAM Journal on Computing 31(2), 331–352 (2001)
Chuzhoy, J., Ostrovsky, R., Rabani, Y.: Approximation algorithms for the job interval selection problem and related scheduling problem. In: Proc. IEEE Symposium on Foundations of Computer Science, pp. 348–356 (2001)
Agarwal, P.K., Sharir, M.: Davenport-Schinzel sequences and their geometric applications. In: Sack, J., Urutia, J. (eds.) Handbook of Computational Geometry. Elsevier Science, Amsterdam (1999)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Asahiro, Y., Miyano, E., Shimoirisa, S. (2005). Pickup and Delivery for Moving Objects on Broken Lines. In: Coppo, M., Lodi, E., Pinna, G.M. (eds) Theoretical Computer Science. ICTCS 2005. Lecture Notes in Computer Science, vol 3701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560586_5
Download citation
DOI: https://doi.org/10.1007/11560586_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29106-0
Online ISBN: 978-3-540-32024-1
eBook Packages: Computer ScienceComputer Science (R0)