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From: gvcormack@watmum.UUCP (Gordon V. Cormack)
Newsgroups: net.lang
Subject: Re: Efficiency of Languages (and comlexity)
Message-ID: <314@watmum.UUCP>
Date: Sun, 3-Nov-85 11:17:53 EST
Article-I.D.: watmum.314
Posted: Sun Nov  3 11:17:53 1985
Date-Received: Mon, 4-Nov-85 01:49:02 EST
References: <15100004@ada-uts.UUCP> <15100007@ada-uts.UUCP> <189@opus.UUCP>
Organization: U of Waterloo, Ontario
Lines: 13

> NO!  You cannot throw "n different processors" at the array!  N is
> (potentially) larger than the number of processors you have.  Actually,
> there is an assumption in analyzing algorithms that one does not have an
> infinite number of computational elements (whatever they may be).  If you
> throw out that assumption, you're nowhere--because (1) you can't build, or
> even emulate, the hardware implied and mostly (2) all the algorithms
> you're going to find interesting will take constant time!  (If you have
> unlimited hardware, you just keep replicating and working in parallel.)

Sorry, this is just not true.  There is inherent sequencing in many
problems.  For example, it is extremely difficult to sort in O(log n)
time using n processors.  Noone knows (and indeed I think it is
impossible) to sort in O(1) time with n log n processors.