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Online Travelling Salesman Problem on a Circle

  • Vinay A. JawgalEmail author
  • V. N. Muralidhara
  • P. S. Srinivasan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11436)

Abstract

In the online version of Travelling Salesman Problem, requests to the server (salesman) may be presented in an online manner i.e. while the server is moving. In this paper, we consider a special case in which requests are located only on the circumference of a circle and the server moves only along the circumference of that circle. We name this problem as online Travelling Salesman Problem on a circle (OLTSP-C). Depending on the minimization objective, we study two variants of this problem. One is the homing variant called H-OLTSP-C in which the objective is to minimize the time to return to the origin after serving all the requests. The other is the nomadic variant called N-OLTSP-C in which after serving all the requests, it is not required to end the tour at the origin. The objective is to minimize the time to serve the last request. For both the problem variants, we present online algorithms and lower bounds on the competitive ratios. An online algorithm is said to be zealous if the server that is used by the online algorithm does not wait when there are unserved requests. For N-OLTSP-C, we prove a lower bound of \(\frac{28}{13}\) on the competitive ratio of any zealous online algorithm and present a 2.5-competitive zealous online algorithm. For H-OLTSP-C, we show how the proofs of some of the known results of OLTSP on general metric space and on a line metric, can be adapted to get lower bounds of \(\frac{7}{4}\) and 2 on the competitive ratios of any zealous and non-zealous online algorithms, respectively.

Keywords

Online algorithms Competitive ratio Travelling Salesman Problem 

Notes

Acknowledgements

We are thankful to Shyam K.B for being part of technical discussions that led to this work and for reviewing this paper.

References

  1. 1.
    Albers, S.: Online algorithms: a survey. Math. Program. 97(1), 3–26 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ascheuer, N., Krumke, S.O., Rambau, J.: Online dial-a-ride problems: minimizing the completion time. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 639–650. Springer, Heidelberg (2000).  https://doi.org/10.1007/3-540-46541-3_53CrossRefGoogle Scholar
  3. 3.
    Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M.: Algorithms for the on-line travelling salesman 1. Algorithmica 29(4), 560–581 (2001)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bjelde, A., et al.: Tight bounds for online tsp on the line. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Philadelphia, PA, USA, pp. 994–1005 (2017)Google Scholar
  5. 5.
    Blom, M., Krumke, S.O., de Paepe, W.E., Stougie, L.: The online tsp against fair adversaries. INFORMS J. Comput. 13(2), 138–148 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Feuerstein, E., Stougie, L.: On-line single-server dial-a-ride problems. Theoret. Comput. Sci. 268(1), 91–105 (2001). On-line Algorithms 1998MathSciNetCrossRefGoogle Scholar
  7. 7.
    Jaillet, P., Wagner, M.R.: Online vehicle routing problems: a survey. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, pp. 221–237. Springer, Boston (2008).  https://doi.org/10.1007/978-0-387-77778-8_10CrossRefGoogle Scholar
  8. 8.
    Lipmann, M.: On-line routing (2003)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vinay A. Jawgal
    • 1
    Email author
  • V. N. Muralidhara
    • 1
  • P. S. Srinivasan
    • 1
  1. 1.IIIT BangaloreBangaloreIndia

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