Abstract
Based on some results of k-server problem and k-taxi problem, the on-line weighted k-taxi problem is originally proposed and studied by our team. In the weighted k-taxi problem, the cost of every taxi on the same distance is different whereas that is same in the traditional k-taxi problem. In this paper, the formulation of the on-line weighted k-taxi problem is presented first. Following that, some preliminary results which used to get the main theorems are given. Thirdly, some on-line algorithms are designed to address the problem and the competitive analysis are given in detail. Furthermore, the lower bound of competitive ratio for some special cases is obtained. Finally, some conclusions are made and some future research directions are pointed out.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for server problems. Journal of Algorithms (11), 208–230 (1990)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communication of the ACM 28, 202–208 (1985)
Fiat, A., Ricklin, M.: Competitive algorithms for the weighted server ploblem. Theoretical Computer Science 130, 85–99 (1994)
Koutsoupias, E., Taylor, D.: The CNN problem and other k-server variants. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 581–592. Springer, Heidelberg (2000)
Chrobak, M., Sgall, J.: The weighted 2-server problem. Theoretical Computer Science 324, 289–312 (2004)
Epstein, L., Imreh, C., van Stee, R.: More on weighted servers or FIFO is better than LRU. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 257–268. Springer, Heidelberg (2002)
Xu, Y.F., Wang, K.L.: On-line k-taxi problem and competitive algorithm (in Chinese). Journal of Xi’an Jiaotong University (1), 56–61 (1997)
Xu, Y.F., Wang, K.L., Ding, J.H.: On-line k-taxi scheduling on a constrained graph and its competitive algorithm. Journal of System Engineering (12), 361–365 (in Chinese) (1999)
Xu, Y.F., Wang, K.L., Zhu, B.: On the k-taxi problem. Information 2(4) (1999)
Xin, C.L., Ma, W.M.: Scheduling for On-line Taxi Problem On a Real Line and Competitive Algorithms. In: ICMLC 2004. Proceedings of the Third International Conference on Machine Learning and Cybernetics, pp. 3078–3084 (2004)
Ma, W.M., Wang, K.: On-line taxi problem on the benefit-cost graphs. In: ICMLC 2006. Proceedings of the Fifth International Conference on Machine Learning and Cybernetics, pp. 900–905 (2006)
Ma, W.M., Wang, K.: On the On-Line k-Truck Problem with Benefit Maximization. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 660–669. Springer, Heidelberg (2006)
Ma, W.M., Xu, Y.F., You, J., Liu, J., Wang, K.L.: On the k-truck scheduling problem. International Journal of Foundations of Computer Science 15(1), 127–141 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, W., Wang, K. (2007). On the On-Line Weighted k-Taxi Problem. In: Chen, B., Paterson, M., Zhang, G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. ESCAPE 2007. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74450-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-74450-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74449-8
Online ISBN: 978-3-540-74450-4
eBook Packages: Computer ScienceComputer Science (R0)