Improved optimal shared memory simulations, and the power of reconsideration

We present time-processor optimal randomized algorithms for simulating a shared memory machine (EREW PRAM) on, a distributed memory machine (DMM). The first algorithm simulates each step of an n-processor EREW PRAM on an n-processor DMM with O(log log n/log log log n) delay with high probability. This simulation is work optimal and can be made time-processor optimal. The best previous optimal simulations require O(log log n) delay. We also study reconfigurable DMMs which are a "complete network version" of the well studied reconfigurable meshes. We show an algorithm that simulates each step of an n-processor EREW PRAM DMM an n-processor reconfigurable DMM with only O(log* n) delay with high probability. We further show how to make this simulation time-processor optimal.<<ETX>>

[1]  Yosi Ben-Asher,et al.  Ranking on Reconfigurable Networks , 1991, Parallel Process. Lett..

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

[3]  Friedhelm Meyer auf der Heide,et al.  Simple, efficient shared memory simulations , 1993, SPAA '93.

[4]  R.M. Karp, M. Luby, F. Meyer auf der Hei.  Efficient PRAM simulation on a distributed memory machine , 1996 .

[5]  Friedhelm Meyer auf der Heide,et al.  Exploiting Storage Redundancy to Speed up Randomized Shared Memory Simulations , 1996, Theor. Comput. Sci..

[6]  Eli Upfal,et al.  How to share memory in a distributed system , 1984, JACM.

[7]  Abhiram G. Ranade,et al.  How to emulate shared memory , 1991, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[8]  Frank Thomson Leighton,et al.  Methods for message routing in parallel machines , 1992, STOC '92.

[9]  Uzi Vishkin,et al.  Recursive Star-Tree Parallel Data Structure , 1993, SIAM J. Comput..

[10]  Eli Upfal,et al.  Parallel hashing: an efficient implementation of shared memory , 1988, JACM.

[11]  Eli Upfal,et al.  Parallel hashing: an efficient implementation of shared memory , 1988, JACM.

[12]  Friedhelm Meyer auf der Heide,et al.  Exploiting Storage Redundancy to Speed up Randomized Shared Memory Simulations , 1995, Theor. Comput. Sci..

[13]  Frank Thomson Leighton,et al.  A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer , 1993, SPAA '93.

[14]  Colin McDiarmid,et al.  Surveys in Combinatorics, 1989: On the method of bounded differences , 1989 .

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

[16]  David Peleg,et al.  The Complexity of Reconfiguring Network Models , 1992, Inf. Comput..

[17]  Yossi Matias,et al.  An optical simulation of shared memory , 1994, SPAA '94.

[18]  Torben Hagerup,et al.  Fast Parallel Space Allocation, Estimation and Integer Sorting , 1995, Inf. Comput..

[19]  Friedhelm Meyer auf der Heide,et al.  A New Universal Class of Hash Functions and Dynamic Hashing in Real Time , 1990, ICALP.

[20]  Friedhelm Meyer,et al.  Hashing strategies for simulating shared memory on distributed memory machines , 1992 .

[21]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[22]  Gen-Huey Chen,et al.  Two-Dimensional Processor Array with a Reconfigurable Bus System is at Least as Powerful as CRCW Model , 1990, Inf. Process. Lett..

[23]  Alan Siegel,et al.  On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications , 1989, 30th Annual Symposium on Foundations of Computer Science.

[24]  Stephan Olariu,et al.  On the Power of Two-Dimensional Processor Arrays with Reconfigurable Bus Systems , 1991, Parallel Process. Lett..

[25]  Friedhelm Meyer auf der Heide,et al.  Hashing Strategies for Simulating Shared Memory on Distributed Memory Machines , 1992, Heinz Nixdorf Symposium.