[comp.parallel] Sort on a NxN Processor Array

fpst@hubcap.UUCP (Steve Stevenson) (01/31/89)

>From: KOLOUTSAKIS%grcrvax1.bitnet@RELAY.CS.NET 
>
>I would appreciate any suggestions, references or solutions 
>for the following problem:
>       We have a SIMD, 4-connected, NxN Mesh Connected Computer (MCC) and
>       the following
>       algorithm for sorting on it. The algorithm is an extension of the
>       so called "odd-even transposition sorting" (OETS) algorithm for a
>       sequence of N processors:
>
>       P <--> P <--> P <--> ... <--> P
>        0      1      2               N-1
>
> ...rest of the article...
>   
>        Michalis Kolountzakis,
>        Math. Dept, Univ. of Crete, Greece

 have made a list of some of the references that mention sorting on
a Mesh-Connected array of processors. I have no idea how these will 
work on a SIMD constrained system. If you can do something with 
odd -vs- even columns and rows, you may be able to do something with
the Shearsort article. I have seen the (OETS) algorithm called 
"Conways Algorithm" in a few journal articles dealing with formalism
in the form of parallel touring machines, but I cannot trace the
reference. If anyone has references to (OETS) or Conway, please send
it on.

Back to the references...

C. D. Thompson and H. T. Kung, "Sorting on a Mesh-Connected Parallel
Computer," Comm. ACM, V20 (Apr 1977), pp 263-271.

D. Nassimi. and S. Sahni, "Bitonic Sort on a Mesh-Connected
Parallel Computer," IEEE Trans. Comp., V27 #1 (Jan 1979).

P. Chen and M. Nussbaum, "Sorting with Systolic Architecture,"
IEEE Parallel Proc., (1985), pp 865-868.

H. Lang, M. Schimmler, H. Schmeck, and H. Schroder, "Systolic Sorting
on a Mesh-Connected Network," IEEE Trans. Comp., V34 #7 (July 1985),
pp 652-658.

Y. Ma, S. Sen, and I. D. Scherson, "The Distance bound on Mesh
-Connected Processor Arrays is Tight," IEEE Parallel Proc., (1986)
pp 255-263.

K. Sado and Y. Igarashi, "Some Parallel Sorts on a Mesh-Connected 
Processor Array and their Time Efficiency," J. Parallel & Dist. Compu.,
V3 (1986), pp 398-410.

C. P. Schnorr and A. Shamir, "An Optimal Sorting Algorithm For Mesh 
Connected Computers," ACM STOC conference (1986), pp 255-263.

Y. Choi adn M. Malek, "A Fault-Tolerant Systolic Sorter," IEEE Trans.
Comp., V37 #5 (May 1988), pp621-624.

I hope some of this helps.
David.

-- 
Steve Stevenson                            fpst@hubcap.clemson.edu
(aka D. E. Stevenson),                     steve@hubcap.clemson.csnet
Department of Computer Science,            comp.parallel
Clemson University, Clemson, SC 29634-1906 (803)656-5880.mabell

halldors@athos.rutgers.edu (Halldorsson) (02/01/89)

In article <4259@hubcap.UUCP> fpst@hubcap.UUCP (Steve Stevenson) writes:

> I have seen the (OETS) algorithm called 
> "Conways Algorithm" in a few journal articles dealing with formalism
> in the form of parallel touring machines, but I cannot trace the
> reference. If anyone has references to (OETS) or Conway, please send
> it on.

If you are referring to the aforementioned mesh version of OETS, then
I'm very interested in seeing those.

If you are referring to the plain OETS (also called "Brickwall sort"),
then Knuth vol.III discusses it, but I believe it originates with
Demuth:
   Demuth: "Electronic Data Sorting". Ph.D. Dissertation, 1956.
   Reprinted in IEEE TOC c-34,April 1985, pp.296

It is also discussed fairly well in these overview references:
  Akl: "Parallel Sorting Algorithms". (Wiley?) 1985

  Lakshmivarahan et al: "Parallel Sorting Algorithms", in Advances in
  Computers, 1984.

  Kronsjo: "Computational Complexity of Sequential and Parallel
Algorithms". Wiley 1985.

> Back to the references...

Good list of references. I can only add two more on mesh sorting:

  Kunde: "Routing&Sorting on Mesh-Connected Arrays", VLSI Algorithms &
  Architecture. Springer LNCS #319

  Leighton: "Tight Bounds on the Complexity of Parallel Sorting". STOC '84
	 Also in IEEE TOC, c-34, 4, April 1985, pp.344


Magnus