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From: sher@rochester.UUCP (David Sher)
Newsgroups: net.lang
Subject: Re: Efficiency of Languages (and comlexity)
Message-ID: <12860@rochester.UUCP>
Date: Sat, 2-Nov-85 23:50:37 EST
Article-I.D.: rocheste.12860
Posted: Sat Nov  2 23:50:37 1985
Date-Received: Mon, 4-Nov-85 03:09:43 EST
References: <15100004@ada-uts.UUCP> <15100007@ada-uts.UUCP> <189@opus.UUCP>
Reply-To: sher@rochester.UUCP (David Sher)
Organization: U. of Rochester, CS Dept.
Lines: 32

In article <189@opus.UUCP> rcd@opus.UUCP (Dick Dunn) writes:
 ...
>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.)
>
 ...
>-- 
>Dick Dunn	{hao,ucbvax,allegra}!nbires!rcd		(303)444-5710 x3086
>   ...At last it's the real thing...or close enough to pretend.

I am afraid that this opinion is an oversimplification.  It is true that 
if you have arbitrary amounts of hardware analysis of algorithms becomes
meaningless (since all problems are table lookup).  However it is 
perfectly reasonable to study the case where the amount of hardware
available is proportional to size of the problem or some function thereof
(like log(n)).  This is no more an assumption of infinite hardware
than O(n) assumes that you have infinite time.  As an example 
consider the result that you can sort at speed O(n) with O(n) hardware.
This means that if you are willing to acquire hardware proportional to the
maximum size of the input you are expecting you can save a log(n) factor
in sorting.  An interesting result no?

-- 
-David Sher
sher@rochester
seismo!rochester!sher