Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83 (MC840302); site boring.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!genrad!teddy!panda!talcott!harvard!seismo!mcvax!boring!paulv From: paulv@boring.UUCP Newsgroups: net.math Subject: Re: Karmarkar algorithm Message-ID: <6285@boring.UUCP> Date: Tue, 15-Jan-85 14:32:58 EST Article-I.D.: boring.6285 Posted: Tue Jan 15 14:32:58 1985 Date-Received: Thu, 17-Jan-85 14:04:55 EST References: <7700001@hplvle.UUCP> Reply-To: paulv@boring.UUCP (Paul Vitanyi) Organization: CWI, Amsterdam Lines: 47 Apparently-To: rnews@mcvax.LOCAL In article <7700001@hplvle.UUCP> drick@hplvle.UUCP (drick) writes: >[bug food] >0. Karmarkar's paper has not been published yet. >1. "A direct comparison of cpu times shows that the new method beats >MPSX/370 - a commercial implementation of the simplex method - by more >than a factor of 50 on problems with several thousand variables. >4. The existence of this algorithm reestablishes Turing's model of >computation. Briefly, Turing said a "good" algorithm is a polynomial- >time algorithm. The only previously known polynomial-time algorithm >for linear programming, the ellipsoid method, was slower in practice >than the simplex method (an exponential-time method), thus casting >doubt on Turing's conjecture. >David L. Rick >Loveland Instrument Division >Hewlett-Packard Company >hplabs!hplvla!hplvle 0. Karmarkar's method appears in the Proceedings of the 16th ACM Symposium on Theory of Computing, Washington D.C., April-May 1984, pp 302-311 (ACM Order #508840). 1. It is claimed to have beaten the blah package for some specific problems, not for all problems. Maybe K's Algorithm runs better only on this eclectic set. 4. The algorithm has not more to do with T's model of computation than any other algorithm. Turing had been dead for over a decade (and his paper published for thirty years) before somebody (Cobham-Hartmanis- Stearns-Cook-Karp '65~'70s) started talking about polynomial time algorithms. The simplexmethod runs in linear time for most *real-life* problems, but can be forced to spend exponential time on some *cooked-up* problems. 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. For *practical* use the simplexmethod appeared to perform better. The Karmarkar algorithm is *claimed* to perform not only better than any other in the *theoretically* interesting *worst-case*, but also in *practical use*. About the latter claim there is no consensus at all; a lot of investigation is going on. The worst-case running time of K's algorithm is worse than what is considered acceptable for a common run of Simplex; the question is whether it in general performs better on common natural problems than does Simplex. Nothing in this story throws, or has thrown, any doubt on Turing's or anybody elses conjectures. It has no bearing on the value of any model of computation.