Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 (MU) 9/23/84; site mulga.OZ
Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!mulga!bjpt
From: bjpt@mulga.OZ (Benjamin Thompson)
Newsgroups: net.math
Subject: Re: Karmarkar algorithm
Message-ID: <612@mulga.OZ>
Date: Thu, 17-Jan-85 19:05:01 EST
Article-I.D.: mulga.612
Posted: Thu Jan 17 19:05:01 1985
Date-Received: Mon, 21-Jan-85 07:54:31 EST
References: <7700001@hplvle.UUCP> <6285@boring.UUCP>
Reply-To: bjpt@mulga.OZ (Benjamin Thompson)
Organization: Comp Sci, Melbourne Uni, Australia
Lines: 14
Summary: 

In article <6285@boring.UUCP> paulv@boring.UUCP (Paul Vitanyi) writes:
>		... 		It was unknown whether LP was as
>difficult as a large class of problems (NP-Complete Problems) for
>which only exponential *worst-case* time algorithms are known. When
>Khachians Ellipsoid Algorithm came along (1979) it was shown
>that LP is not difficult, in that sense, i.e., the latter algorithm
>has a polynomial worst-case running time.


Khachian's algorithm being polynomial time does *not* mean that LP is not
an NP-complete problem.  To draw this conclusion, one has to make the
as-yet *unproven* assumption that NP is not equal to P.

			Ben Thompson, {decvax,vax135}!mulga!bjpt