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Subject: Re: An Interesting Aspect To The Travelling Salesman Problem

Author: Robert Hyatt

Date: 06:41:14 05/18/01

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On May 18, 2001 at 04:17:59, Graham Laight wrote:

>On May 17, 2001 at 22:22:48, Robert Hyatt wrote:
>
>>The traveling salesman problem is well-known.  Route a salesman through N
>>cities with the shortest total travel time possible.  Since the number of
>>cities on Earth are limited, and since the number of cities that a traveling
>>salesman would actually need to visit is even more limited, it is a finite
>>problem.  As I said before, I don't care about visiting the moons of
>>Jupiter or Mars, nor planets around alpha-centauri, etc.
>>
>>To the traveling salesman, the problem is finite.  Yet the complexity makes it
>>intractable even for reasonable numbers of cities.  Just try the county seats
>>of government for every county or parish in the US.  Not with today's computers.
>>Not with next year's either.  Or next century's.  Yet that is smaller than
>>chess.
>
>One thing that fascinates me about the travelling salesman problem is this: why
>is it that it is so difficult to calculate with simple programs, and yet... if
>you draw a two dimensional map and put the towns on as points, it's easy to draw
>out an efficient route between the towns.
>
>This is an excellent example of an instance where the computers are
>uncompetitive because the humans are doing something that seems simple to them -
>but they don't actually know what they're doing, so they can't program computers
>to do it.
>
>-g


I think you will find it harder to do with that 2D map than you realize.
Remember, you are trying to find the _shortest_ path.  not one of several
thousand "almost shortest"...



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