in reply to Travelling problem

Are you aware that

Please check if you really need all criteria!

Pick at most 2 of 3 and we might be able to help:

If it's just a theoretical question and you can't limit the requirements, then I suppose a branch and bound algorithm might be the best approach, but it won't be faster than brute force in some edge cases.

HTH! =)

Cheers Rolf

( addicted to the Perl Programming Language)

update

had a short glance at the WP article and it describes much better what I wanted to tell.

footnotes

¹) almost

²) corrected, educated foo++

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Re^2: Travelling problem
by educated_foo (Vicar) on Dec 22, 2013 at 00:54 UTC
    Fast (i.e. non-polynomial) computation
    You mean "i.e. polynomial," right? NP is exponential ;-). I heartily agree with your post, and defer to my favorite MJD talk for the details.

    EDIT: Nut graph:

    next time someone tells you to give up on your problem because it's NP-complete, ignore them.
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      > You mean "i.e. polynomial,"

      yes, kind of "non-exponential" =)

      Was a short night! :)

      Cheers Rolf

      ( addicted to the Perl Programming Language)

      update

      > next time someone tells you to give up on your problem because it's NP-complete, ignore them.

      Unfortunately well described problems are rare here.

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        Unfortunately well described problems are rare here.
        As are honestly thoughtful and helpful responses, and genuine discussion. As someone who has been here awhile (perhaps far too long), I know how to separate the wheat-y help from the karma-whoring chaff (I've contributed to both). New users, however, may not know how to filter out the mindless nostrums.
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Re^2: Travelling problem
by Dirk80 (Pilgrim) on Dec 21, 2013 at 21:12 UTC

    Yes, you are right. The "travelling salesman problem" exactly describes my problem. Thank you!!!

    I have 24 places and I know the distance between these places in km. I have to visit the first place, then 22 places in any order and then the 24th place. I don't need a perfect solution. I just want to find a short way, not the shortest one. And the computation time should not be too long. An approximation is enough.

[reply]
      The Christofides Algorithm mentioned by educated foo guaranties a solution better than 1.5 times the optimum.

      Nota bene: since you have a fixed start and end for an "open" hamiltonian path (i.e. not a circle like in the TSP) you'll need to adjust the algorithm accordingly. ¹

      Cheers Rolf

      ( addicted to the Perl Programming Language)

      update

      ¹) after reading two SO discussions (search "minimal hamilton path") you just need to add a dummy point neighboring (only) the desired start- and end-point with distance 0 (!)

      Like this any TSP algorithm will chose start and end as neighbors for a hamilton circle with the same accumulated length like a optimized hamilton path, you just need to ignore the two dummy edges at the end.

[reply]
      I have 24 places and I know the distance between these places in km. I have to visit the first place, then 22 places in any order and then the 24th place.

      Could you post a sample dataset?

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
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