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From: vannoord@let.rug.nl (Gertjan van Noord)
Subject: Re: Minimum value of predicate? (Efficiency)
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Message-ID: <1997Jan27.140001.9455@let.rug.nl>
Date: Mon, 27 Jan 1997 14:00:01 GMT
References: <32DD1DC9.47E6@info.ucl.ac.be> <pereira-2001972020370001@baldy.research.att.com> <5cglet$9g6@mulga.cs.mu.OZ.AU>
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>pereira@research.att.com (Fernando Pereira) writes:
>
>But also "in practice", many algorithms that are worse than O(n log n) are
>used on data that does not exercise their worst-case behavior. It would be
>of course nice to be able to prove that the actual data are in restricted
>classes for which the algorithm has better worst-case behavior, but that
>is either untrue or very hard to prove. Here are a few examples in which
>algorithms with poor worst-case behavior are used on large problems
>successfully because of the nature of the data:
>
>- graph and map layout
>- automata determinization
>- model-checking of (finite-state) specifications
>- traveling salesman
>- set cover
>- boolean satisfiability using randomized local search
>
>I can get you references on applications of these to large industrial
>problems. In fact, I would contend that the O(N) and O(N log N) algorithms
>are just basic scaffolding and that the interesting *real* problems are
>the computationally hard ones.

I fully agree with the main point. However, I am surprised to see
traveling salesman in this list. Isn't it the case that in any 
serious application approximation algorithms are used (which typically
do not guarantee best solution) rather than, say, an A-star kind of
algorithm? In my (limited) experience traveling salesman is one of
those problems in which almost all instances _are_ extremely hard
to solve within reasonable time bounds. 

-- 
dr Gertjan van Noord Alfa-informatica, RUG, Postbus 716, 9700 AS Groningen
vannoord@let.rug.nl      tel. +31-50-3635935      fax  +31-50-3636855
http://www.let.rug.nl/~vannoord/
