Average Case Analyses of List Update Algorithms, with Applications to Data Compression

Abstract. We study the performance of the Timestamp (0) (TS(0)) algorithm for self-organizing sequential search on discrete memoryless sources. We demonstrate that TS(0) is better than Move-to-front on such sources, and determine performance ratios for TS(0) against the optimal off-line and static adversaries in this situation. Previous work on such sources compared on-line algorithms only with static adversaries. One practical motivation for our work is the use of the Move-to-front heuristic in various compression algorithms. Our theoretical results suggest that in many cases using TS(0) in place of Move-to-front in schemes that use the latter should improve compression. Tests using implementations on a standard corpus of test documents demonstrate that TS(0) leads to improved compression.

[1]  Boris Teia,et al.  A Lower Bound for Randomized List Update Algorithms , 1993, Inf. Process. Lett..

[2]  Gaston H. Gonnet,et al.  Toward self-organizing linear search , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[3]  Susanne Albers,et al.  Improved randomized on-line algorithms for the list update problem , 1995, SODA '95.

[4]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[5]  Ramarathnam Venkatesan,et al.  Splay trees for data compression , 1995, SODA '95.

[6]  Jon Louis Bentley,et al.  Amortized analyses of self-organizing sequential search heuristics , 1985, CACM.

[7]  Robert E. Tarjan,et al.  A Locally Adaptive Data , 1986 .

[8]  Ronald L. Rivest,et al.  On self-organizing sequential search heuristics , 1976, CACM.

[9]  D. J. Wheeler,et al.  A Block-sorting Lossless Data Compression Algorithm , 1994 .

[10]  V. Rich.  Personal communication , 1989, Nature.

[11]  Alan Weiss,et al.  Large Deviations For Performance Analysis: Queues, Communication and Computing , 1995 .

[12]  Gaston H. Gonnet,et al.  Exegesis of Self-Organizing Linear Search , 1981, SIAM J. Comput..

[13]  Ran El-Yaniv,et al.  Online list accessing algorithms and their applications: recent empirical evidence , 1997, SODA '97.

[14]  Paul D. Seymour,et al.  Self-organizing sequential search and Hilbert's inequalities , 1985, Symposium on the Theory of Computing.

[15]  Sandy Irani,et al.  Two Results on the List Update Problem , 1991, Inf. Process. Lett..

[16]  Jeffery R. Westbrook,et al.  Randomized competitive algorithms for the list update problem , 1991, SODA '91.

[17]  Nabil Kahale.  Large Deviation Bounds for Markov Chains , 1997, Comb. Probab. Comput..

[18]  Michel Mandjes,et al.  Large Deviations for Performance Analysis: Queues, Communications, and Computing , Adam Shwartz and Alan Weiss (New York: Chapman and Hall, 1995). , 1996, Probability in the Engineering and Informational Sciences.