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A Transposition Rule Analysis Based on a Particle Process

Part of: Limit theorems Theory of data

Published online by Cambridge University Press:  14 July 2016

David Gamarnik  and
Petar Momčilović
David Gamarnik*
Affiliation:
IBM T. J. Watson Research Center
Petar Momčilović
Affiliation:
IBM T. J. Watson Research Center
*
∗Postal address: Department of Mathematical Sciences, IBM T. J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598, USA. Email address: gamarnik@watson.ibm.com
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Abstract

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A linear list is a collection of items that can be accessed sequentially. The cost of a request is the number of items that need to be examined before the desired item is located, i.e. the distance of the requested item from the beginning of the list. The transposition rule is one of the algorithms designed to reduce the search cost by organizing the list. In particular, upon a request for a given item, the item is transposed with the preceding one. We develop a new approach for analyzing the algorithm, based on a coupling to a certain constrained asymmetric exclusion process. This allows us to establish an asymptotic optimality of the rule for two families of request distributions.

Keywords

Self-organizing listaverage-case analysisexclusion process

MSC classification

Secondary: 68P05: Data structures 68P10: Searching and sorting 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 235 - 246
Copyright
© Applied Probability Trust 2005 

Footnotes

∗∗

Current address: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA. Email address: petar@eecs.umich.edu

References

Anderson, E., Nash, P. and Weber, R. (1982). A counterexample to a conjecture in optimal list ordering. J. Appl. Prob. 19, 730–732.CrossRefGoogle Scholar
Bachrach, R. and El-Yaniv, R. (1997). Online list accessing algorithms and their applications: Recent empirical evidence. In Proc. Eighth Annual Symp. Discrete Algorithms (New Orleans, LA), ACM, New York, pp. 53–62.Google Scholar
Barrera, J. and Paroissin, C. (2004). On the distribution of the search cost for the move-to-front rule with random weights. J. Appl. Prob. 41, 250–262.CrossRefGoogle Scholar
Fill, J. (1996). An exact formula for the move-to-front rule for self-organizing lists. J. Theoret. Prob. 9, 113–159.CrossRefGoogle Scholar
Fill, J. (1996). Limits and rates of convergence for the distribution of search cost under the move-to-front rule. Theoret. Comput. Sci. 164, 185–206.CrossRefGoogle Scholar
Fill, J. and Holst, L. (1996). On the distribution of search cost for the move-to-front rule. Random Structures Algorithms 8, 179–186.3.0.CO;2-V>CrossRefGoogle Scholar
Flajolet, P., Gardy, D. and Thimonier, L. (1992). Birthday paradox, coupon collector, caching algorithms and self-organizing search. Discrete Appl. Math. 39, 207–229.CrossRefGoogle Scholar
Hester, J. and Hirchberg, D. (1985). Self-organizing linear search. Comput. Surveys 17, 295–311.CrossRefGoogle Scholar
Jelenković, P. (1999). Asymptotic approximation of the move-to-front search cost distribution and least-recently-used caching fault probabilities. Ann. Appl. Prob. 9, 430–464.CrossRefGoogle Scholar
Kan, Y. and Ross, S. (1980). Optimal list order under partial memory constraints. J. Appl. Prob. 17, 1004–1015.CrossRefGoogle Scholar
Knuth, D. (1998). The Art of Computer Programming, Vol. 3, 2nd edn. Addison-Wesley, Reading, MA.Google Scholar
Lam, K., Leung, M. Y. and Siu, M. K. (1984). Self-organizing files with dependent accesses. J. Appl. Prob. 21, 343–359.CrossRefGoogle Scholar
Rivest, R. (1976). On self-organizing sequential search heuristics. Commun. ACM 19, 63–67.CrossRefGoogle Scholar
Sleator, D. and Tarjan, R. (1985). Amortized efficiency of list update and paging rules. Commun. ACM 28, 202–208.CrossRefGoogle Scholar
Tenenbaum, A. and Nemes, R. (1982). Two spectra of self-organizing sequential search algorithms. SIAM J. Comput. 11, 557–566.CrossRefGoogle Scholar