Optimal constant space move-to-fear list organization
We consider the problem of adaptively organizing a list whose elements are accessed with a fixed but unknown probability distribution. We present a strategy which has constant additional space requirements and which achieves the reorganization by performing a data restructuring operation on an element exactly once. The scheme, which is stochastically absorbing, and is of a Move-to-Rear flavour is shown to be asymptotically optimal. In other words, by suitably performing the Move-to-Rear operation the probability of converging to the optimal arrangement can be made as close to unity as desired. Considering all of these features, this strategy is probably the most ideal list organization strategy reported in the literature. Simulation results demonstrating the power of the scheme have been included. The paper also includes a hybrid data reorganization scheme in which an absorbing Move-To-Rear rule and an ergodic rule are used in conjunction with each other.
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- Arnow, D.M. and Tenebaum, A.M., "An Investigation of the Move-Ahead-k Rules", Congressus Numerantium, Proc. of the Thirteenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida, February 1982, pp. 47–65.Google Scholar
- Burville, P.J. and Kingman, J.F.C., "On a Model for Storage and Search", J. Appl. Probability, Vol.10, 1973, pp. 697–701.Google Scholar
- Hendricks, W.J., "An Extension of a Theorem Concerning an Interesting Markov Chain", J. App. Probability, Vol.10, 1973, pp.231–233.Google Scholar
- Kan, Y.C. and Ross, S.M., "Optimal List Order Under Partial Memory Constraints", J. App. Probability, Vol.17, 1980, pp. 1004–1015.Google Scholar
- Isaacson, D.L. and Madsen, R.W., "Markov Chains: Theory and Applications" New York, John Wiley & Son, 1976.Google Scholar
- Knuth, D.E., "The Art of Computer Programming, Vol.3, Sorting and Searching", Addison-Wesley, Reading, MA., 1973.Google Scholar
- McCabe, J., "On Serial Files With Relocatable Records", Operations Research, Vol.12, 1965, pp.609–618.Google Scholar
- Oommen, B.J. and Hansen, E.R., "List Organizing Strategies Using Stochastic Move-to-front and Stochastic Move-to-Rear Operations", to appear in SIAM Journal on Computing. Vol. 16, (1987), 705–716.Google Scholar
- Oommen, B.J., Hansen, E.R. and Munro, J.I., "Deterministic Optimal and Expedient Move-To-Rear List Organizing Strategies", to appear in Theoretical Computer Science (Preliminary abridged version was published in the Proc. of the 25th Annual Allerton Conference, Urbana, Illinois, Sept/Oct. 1987, pp.54–63).Google Scholar
- Sleator, D. and Tarjan, R., "Amortized Efficiency of List Update Rules", Proc. of the Sixteenth Annual ACM Symposium on Theory of Computing, April 1984, pp. 488–492.Google Scholar
- Oommen, B.J., Ng, D.T.H., "Ideal List Organization for Stationary Environments", Submitted for publication. Also available as a Technical Report from the School of Computer Science, Carleton University, Ottawa K1S 5B6, CANADA.Google Scholar