A General Class of Resource Tradeoffs

Abstract In this paper, we study a class of resource tradeoffs that arise in such problems as parallel sorting algorithms, linear recursion schemata, VLSI layouts, and searching algorithms. The tradeoffs can all be traced to the common structure of a multiway tree, and the special class of binomial trees (which are structurally related to the binomial coefficients) correspond to particularly efficient algorithms. Although most of the tradeoff's that we exhibit are upper bounds, we present several examples to show that the approach can also lead to lower bounds.

[1]  Edward M. Reingold,et al.  Efficient generation of the binary reflected gray code and its applications , 1976, CACM.

[2]  Allan Borodin,et al.  A time-space tradeoff for sorting on non-oblivious machines , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[3]  Nicholas Pippenger.  A Time-Space Trade-Off , 1978, JACM.

[4]  Jon Louis Bentley,et al.  Decomposable Searching Problems I: Static-to-Dynamic Transformation , 1980, J. Algorithms.

[5]  Daniel S. Hirschberg.  Fast parallel sorting algorithms , 1978, CACM.

[6]  Joseph JáJá,et al.  Time-space tradeoffs for some algebraic problems , 1980, STOC '80.

[7]  Arnon Rosenthal.  Optimal Algorithms for Sensitivity Analysis in Associative Multiplication Problems , 1981, Theor. Comput. Sci..

[8]  Wolfgang Janko.  Hierarchic Index Sequential Search with Optimal Variable Block Size and Its Minimal Expected Number of Comparisons , 1979, ICALP.

[9]  John E. Savage,et al.  Space-time trade-offs on the FFT algorithm , 1978, IEEE Trans. Inf. Theory.

[10]  Andrew Chi-Chih Yao,et al.  An Almost Optimal Algorithm for Unbounded Searching , 1976, Inf. Process. Lett..

[11]  Ben Shneiderman.  Jump searching: a fast sequential search technique , 1978, CACM.

[12]  Jean Vuillemin,et al.  A data structure for manipulating priority queues , 1978, CACM.

[13]  Robert Melville.  An Improved Simulation Result for Ink-Bounded Turing Machines , 1981, J. Comput. Syst. Sci..

[14]  Ashok K. Chandra.  Efficient Compilation of Linear Recursive Programs , 1973, SWAT.

[15]  Chak-Kuen Wong,et al.  On the Complexity of Permuting Records in Magnetic Bubble Memory Systems , 1980, IBM J. Res. Dev..

[16]  Robert E. Tarjan,et al.  Upper and lower bounds on time-space tradeoffs , 1979, STOC '79.

[17]  Allan Borodin,et al.  A time-space tradeoff for sorting on a general sequential model of computation , 1980, STOC '80.

[18]  C. Thomborson,et al.  Area-time complexity for VLSI , 1979, STOC.

[19]  Franco P. Preparata,et al.  New Parallel-Sorting Schemes , 1978, IEEE Transactions on Computers.