Generalized Swap-with-Parent Schemes for Self-Organizing Sequential Linear Lists

Self organizing linear search algorithms have been in the literature for over 30 years, and numerous schemes have been proposed during that time. Among all the previous algorithms, the move-to-front rule and the transposition rule are the most extensively analyzed schemes. Recently we proposed and thoroughly analyzed a new scheme, the swap-with-parent rule, which views the list as a heap structure with no ordering constraints between parents and their children [12]. From the analyses of the transposition rule and the swap-with-parent rule, it can be seen that the fundamental property of the corresponding Markov chain being time reversible greatly simplifies the analysis of the algorithm. In this paper, we shall show the existence of a class of time reversible Markov chains resulting from performing swaps on “implicit” trees (called ss_trees) which generalize and extend the results concerning the transposition and the swap-with-parent heuristics.

[1]  B. John Oommen,et al.  An Optimal Absorbing List Organization Strategy with Constant Memory Requirements , 1993, Theor. Comput. Sci..

[2]  S. M. Ross,et al.  Optimal list order under partial memory constraints , 1980, Journal of Applied Probability.

[3]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[4]  Charles U. Martel,et al.  Unsuccessful Search in Self-Adjusting Data Structures , 1993, J. Algorithms.

[5]  James R. Bitner,et al.  Heuristics That Dynamically Organize Data Structures , 1979, SIAM J. Comput..

[6]  B. John Oommen,et al.  Deterministic Optimal and Expedient Move-to-Rear List Organizing Strategies , 1990, Theor. Comput. Sci..

[7]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[8]  Aaron M. Tenenbaum,et al.  Two Spectra of Self-Organizing Sequential Search Algorithms , 1982, SIAM J. Comput..

[9]  John McCabe,et al.  On Serial Files with Relocatable Records , 1965 .

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

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

[12]  Daniel S. Hirschberg,et al.  Self-organizing linear search , 1985, CSUR.

[13]  W. J. Hendricks.  An extension of a theorem concerning an interesting Markov chain , 1973 .

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

[15]  B. John Oommen,et al.  List Organizing Strategies Using Stochastic Move-to-Front and Stochastic Move-to-Rear Operations , 1987, SIAM J. Comput..

[16]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .

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