On a Compaction Theorem of Ragde

Ragde demonstrated that in constant time a PRAM with n processors can move at most k items, stored in distinct cells of an array of size n, to distinct cells in an array of size at most k4. We show that the exponent of 4 in the preceding sentence can be replaced by any constant greater than 1.

[1]  L FredmanMichael,et al.  Storing a Sparse Table with 0(1) Worst Case Access Time , 1984 .

[2]  Torben Hagerup,et al.  The Log-Star Revolution , 1992, STACS.

[3]  Richard Cole,et al.  Faster Optimal Parallel Prefix Sums and List Ranking , 2011, Inf. Comput..

[4]  János Komlós,et al.  Storing a sparse table with O(1) worst case access time , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[5]  Michael T. Goodrich.  Using approximation algorithms to design parallel algorithms that may ignore processor allocation , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[6]  David Eppstein,et al.  Parallel Algorithmic Techniques for Combinatorial Computation , 1988, ICALP.

[7]  Uzi Vishkin,et al.  Towards a theory of nearly constant time parallel algorithms , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[8]  Johan Håstad,et al.  Optimal bounds for decision problems on the CRCW PRAM , 1987, STOC.

[9]  Rajeev Raman,et al.  The Power of Collision: Randomized Parallel Algorithms for Chaining and Integer Sorting , 1990, FSTTCS.

[10]  Prabhakar Ragde,et al.  The Parallel Simplicity of Compaction and Chaining , 1990, J. Algorithms.

[11]  Uzi Vishkin,et al.  Converting high probability into nearly-constant time—with applications to parallel hashing , 1991, STOC '91.

[12]  Torben Hagerup,et al.  Fast and Optimal Simulations between CRCW PRAMs , 1992, STACS.

[13]  Torben Hagerup.  Fast Parallel Generation of Random Permutations , 1991, ICALP.

[14]  Torben Hagerup,et al.  Fast and reliable parallel hashing , 1991, SPAA '91.