Abstract
The time-dependent orienteering problem is dual to the time-dependent traveling salesman problem. It consists in visiting a maximum number of sites within a given deadline. The traveling time between two sites is in general dependent on the starting time.
We provide a (2 + ε)-approximation algorithm for the time-dependent orienteering problem which runs in polynomial time if the ratio between the maximum and minimum traveling time between any two sites is constant. No prior upper approximation bounds were known for this time-dependent problem.
The work of the first author was done while he was at the Centro de Modelamiento Matemático, Universidad de Chile and UMR 2071-CNRS, supported by FONDAP and while he was a visiting postdoc at DIMATIA-ITI partially supported by GACR 201/99/0242 and by the Ministry of Education of the Czech Republic as project LN00A056. Also this work was supported by the RFBR grant N01-01-00235.
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References
E. M. Arkin, J. S. B. Mitchell, AND G. Narasimhan, Resource-constrained geometric network optimization, in Proceedings Fourteenth ACM Symposium on Computational Geometry, June 6–10, 1998, pp. 307–316.
B. Awerbuch, Y. Azar, A. Blum, AND S. Vempala, Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesman, in Proceedings 27th Annual ACM Sympos. Theory Comput. (STOC 95), pp. 277–283, 1995.
E. Balas, The prize collecting traveling salesperson problem, Networks, 19, pp. 621–636, 1989.
H.J. Bockenhauer, J. Hromkovic, R. Klasing, S. Seibert, AND W. Unger, An improved lower bound on the approximability of metric TSP and approximation algorithms for the TSP with sharpened triangle inequality, in Proceedings 17th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Springer Verlag, pp. 111–112, 2000.
B. Broden, Time Dependent Traveling Salesman Problem, M.Sc. thesis, Department of Computer Science, Lund University, Sweden, 2000.
J. Cheriyan and R. Ravi, Approximation algorithms for network problems, manuscript, 1998. (http://www.gsia.cmu.edu/andrew/ravi/home.html)
A. Czumaj, I. Finch, L. Gasieniec, A. Gibbons, P. Leng, W. Rytter, AND M. Zito, Efficient Web Searching Using Temporal Factors, in Proceedings of the 6th Workshop on Algorithms and Data Structures (WADS), F. Dehne, A. Gupta, J.-R. Sack, and R. Tamassia, eds., Springer Verlag, Lecture Notes in Computer Science, vol. 1663, 1999, pp. 294–305.
L. Engebretsen, An explicit lower bound for TSP with distances one and two, in Proceedings 16th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, Springer Verlag, pp. 373–382, 1999.
B. G. Golden, L. Levy, AND R. Vohra, The orienteering problem, Naval Res. Logistics, 34 (1991), pp. 307–318.
M. Hammar AND B. Nilsson, Approximation results for kinetic variants of TSP, in Proceedings of the 26th International Colloquium on Automata, Languages, and Programming (ICALP’99), Springer Verlag, Lecture Notes in Computer Science, vol. 1644, 1999, pp. 392–401.
D. S. Johnson, M. Minkoff, AND S. Phillips, The Prize Collecting Steiner Tree Problem: Theory and Practice, Proc. 11th Ann. ACM-SIAM Symp. on Discrete Algorithms, (2000), pp. 760–769.
M. V. Marathe, R. Ravi, R. Sundaram, S. S. Ravi, D. J. Rosenkrantz, H. B. Hunt III, Bicriteria network design problems, J. Algorithms 28 (1998), pp. 142–171.
C.H. Papadimitriou AND S. Vempala, On the approximability of the traveling salesman problem, in Proceedings of the the thirty second ACM STOC, pp. 126–133, 2000.
C.H. Papadimitriou AND M. Yannakakis, The traveling salesman problem with distances one and two, in Mathematics of Operations Research 18(1), pp. 1–11, 1993.
F. C. R. Spieksma, On the approximability of an interval scheduling problem, Journal of Scheduling 2 (1999), pp. 215–227.
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Fomin, F.V., Lingas, A. (2001). Approximation Algorithms for Time-Dependent Orienteering. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_57
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DOI: https://doi.org/10.1007/3-540-44669-9_57
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