Abstract
In this paper the problem of efficiently serving a sequence of requests that are presented in a metric space in an on-line fashion and then returning back to the departure point is considered. The problem is the on-line version of a variant of the Traveling Salesman Problem (namely the Vehicle Routing Problem with release times), and we call it the On-Line Traveling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics.
After proving a ≈ 1.64 lower bound on the competitive ratio that can be achieved by on-line algorithms for OLTSP, two competitive algorithms are shown, one of which is 2-competitive and works for any metric space. The second one allows to achieve a nearly optimal competitive ratio of 1.75 on the real line.
This work was partly supported by ESPRIT BRA Alcom II under contract No.7141, by Italian Ministry of Scientific Research Project 40% “Algoritmi, Modelli di Calcolo e Strutture Informative”, and by a grant from the SCIENCE project “Algorithmic Approaches to Large and Complex Combinatorial Optimization Problems”.
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References
M. Atallah and S. Kosaraju, “Efficient solutions for some transportation problems with application to minimizing robot arm travel”, SIAM J. on Computing, 17 (1988), pp. 849–869.
G. Ausiello, E. Feuerstein, S. Leonardi, L. Stougie, M. Talamo, “Serving requests with on-line routing”, Proc. of the 4th Scandinavian Workshop on Algorithm Theory, LNCS 824.
R. El-Yaniv, A. Fiat, R.M. Karp and G. Turpin, “Competitive analysis of financial games”, Proc. 33rd Annual Symposium on Foundations of Computer Science (1992), pp. 327–333.
M. Garey, and D. Johnson, Computers and intractability: a guide to the theory of NP-completeness, Freeman, San Francisco (1979).
Y. Karuno, H. Nagamochi and T. Ibaraki, “Vehicle scheduling on a tree with release times and handling times”, Proc. 4th. International Symposium on Algorithms and Computation ISAAC'93, LNCS 762 (1993), Springer-Verlag, pp. 486–495.
B. Kalyanasundaram and K.R. Pruhs, “Constructing competitive tours from local information”, Proc. 20th International Colloquium on Automata, Languages and Programming, LNCS 700 (1993), Springer-Verlag.
M. Manasse, L.A. McGeoch and D. Sleator, “Competitive algorithms for server problems”, Journal of Algorithms 11 (1990), pp. 208–230.
H. Psaraftis, M. Solomon, T. Magnanti and T. Kim, “Routing and scheduling on a shoreline with release times”, Management Science 36-2 (1990), pp. 212–223.
D.B. Shmoys, J. Wein, D.P. Williamson, “Scheduling parallel machines on-line”, Proc. of the 32nd Annual Symposium on Foundations of Computer Science, 1991.
D. Sleator, R. Tarjan, “Amortized efficiency of list update and paging rules”, Comm. ACM 28 (1985), pp. 202–208.
M. Solomon and J. Desrosiers, “Time window constrained routing and scheduling problems: a survey”, Transportation Science, 22 (1988), pp. 1–13.
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© 1995 Springer-Verlag Berlin Heidelberg
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Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M. (1995). Competitive algorithms for the on-line traveling salesman. In: Akl, S.G., Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1995. Lecture Notes in Computer Science, vol 955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60220-8_63
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DOI: https://doi.org/10.1007/3-540-60220-8_63
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