Abstract
Maintaining a monotonic labeling of an ordered list during the insertion of n items requires Ω(n log n) individual relabelings, in the worst case, if the number of usable labels is only polynomial in n. This follows from a lower bound for a new problem, prefix bucketing.
This paper is based on a portion of the third author's doctoral dissertation [Zh93], The first author was supported in part by the National Science Foundation under grant CCR-8909667.
We thank Jun Tarui and loan Macarie for their corrections and suggestions.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Andersson, A., Lai, T. W.: Fast updating of well-balanced trees. In: SWAT 90: 2nd Scandinavian Workshop on Algorithm Theory, Proceedings. (Lecture Notes in Computer Science, vol. 447.) Springer, New York Berlin Heidelberg, 1990, pp. 111–121
Dietz, P. F.: Maintaining order in a linked list. In: Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing. Association for Computing Machinery, New York, 1982, pp. 122–127
Dietz, P. F., Sleator, D. D.: Two algorithms for maintaining order in a list. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing. Association for Computing Machinery, New York, 1987, pp. 365–372 (revision to appear in Journal of Computer and System Sciences)
Dietz, P. F., Seiferas, J. I., Zhang, J.: Lower bounds for smooth list labeling, (in preparation)
Dietz, P. F., Zhang, J.: Lower bounds for monotonie list labeling. In: SWAT 90: 2nd Scandinavian Workshop on Algorithm Theory, Proceedings. (Lecture Notes in Computer Science, vol. 447.) Springer, New York Berlin Heidelberg, 1990, pp. 173–180
Hennie, F. C., Stearns, R. E.: Two-tape simulation of multitape Turing machines. Journal of the Association for Computing Machinery 13 (1966) 533–546
Itai, A., Konheim, A. G., Rodeh, M.: A sparse table implementation of sorted sets. IBM Thomas J. Watson Research Center, Yorktown Heights, New York, Research Report RC 9146, 1981
Tsakalidis, A. K.: Maintaining order in a generalized linked list. Acta Informatica 21 (1984) 101–112
Zhang, J.: Density control and on-line labeling problems. Computer Science Department, University of Rochester, Rochester, New York, Technical Report 481 and Ph. D. Thesis, 1993
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dietz, P.F., Seiferas, J.I., Zhang, J. (1994). A tight lower bound for on-line monotonic list labeling. In: Schmidt, E.M., Skyum, S. (eds) Algorithm Theory — SWAT '94. SWAT 1994. Lecture Notes in Computer Science, vol 824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58218-5_12
Download citation
DOI: https://doi.org/10.1007/3-540-58218-5_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58218-2
Online ISBN: 978-3-540-48577-3
eBook Packages: Springer Book Archive