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