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A Transposition Rule Analysis Based on a Particle Process

Part of: Theory of data Limit theorems

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

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