Re: Worst Case Greedy Walk

From	Steve Thompson <thomps2048@yahoo.ca>
Newsgroups	comp.programming, comp.theory, sci.math, comp.graphics.algorithms
Subject	Re: Worst Case Greedy Walk
Date	2011-11-01 20:56 -0400
Organization	A poorly organized news site.
Message-ID	<AuXJNe.Y0A.vgVwo@invalid.invalid> (permalink)
References	<10a6051c-903f-4fd4-95e9-15e90dee066c@m19g2000yqh.googlegroups.com> <4d432c49-dc17-4649-8c0f-06d8490cc96e@g27g2000pre.googlegroups.com>

Cross-posted to 4 groups.

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On Tue, Nov 01, 2011 at 02:29:09PM -0700, Graham Cooper wrote:
> On Nov 1, 1:11 am, Andrew Tomazos <and...@tomazos.com> wrote:
> > I've reduced down a problem I am having in a project I am working on
> > to the following...
> >
> > Given an integer n > 1
> >
> > Let S(n) be a set of n points in the euclidean unit square:
> >
> > ie { {x1, y1}, {x2, y2}, ..., {xn, yn} } all xi and yi are real
> > numbers between 0 and 1 inclusive
> >
> > such that the total distance of the path traveled by starting at the
> > first point and moving directly to the nearest unvisited point (until
> > they have all been visited) is maximized
> >
> > S(2) is { {0,0}, {1,1} } total distance traveled is sqrt(2), we travel
> > from {0,0} to {1,1} diagonally across the square.
> >
> > S(3) is { {0,0}, {0,1}, {1,0} } total distance travelled is 1 +
> > sqrt(2), we travel up side of square from {0,0} to {0,1} for distance
> > of 1, then across square to {1,1}
> >
> > S(4) is { {0,0}, {0,1}, {1,0}, {1,1} } total distance travelled is 3,
> > we travel up from {0,0} to {0,1} then across to {1,1} then down to
> > {1,0}
> >
> > S(5) (I suspect, but am not sure) is { {0.5,0.5}, {0,0}, {0,1}, {1,0},
> > {1,1} } total distance travelled is 3 + sqrt(0.5)
> >
> > The goal would be to efficiently compute S(n) for arbitrary n
> >
> > Is there any way to calculate this set directly in some sort of closed
> > form, or failing that can you think of a linear algorithm? polynomial?
> > approximation?
> >
> > Does this problem reduce to some well-known problem? How?
> >
> > What approach would you recommend?
> >
> > Thanks for your time.  Any thoughts appreciated.
> >
> > Regards,
> > Andrew.
> 
> a (square) spiral

Too obvious?  What about triangles?





Steve Thompson

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Thread

Worst Case Greedy Walk Andrew Tomazos <andrew@tomazos.com> - 2011-10-31 08:11 -0700
  Re: Worst Case Greedy Walk William Elliot <marsh@rdrop.com> - 2011-10-31 21:24 -0700
    Re: Worst Case Greedy Walk Andrew Tomazos <andrew@tomazos.com> - 2011-11-01 12:41 -0700
      Re: Worst Case Greedy Walk William Elliot <marsh@rdrop.com> - 2011-11-01 20:32 -0700
  Re: Worst Case Greedy Walk "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2011-11-01 07:21 +0000
    Re: Worst Case Greedy Walk James Dow Allen <jdallen2000@yahoo.com> - 2011-11-01 00:45 -0700
      Re: Worst Case Greedy Walk Andrew Tomazos <andrew@tomazos.com> - 2011-11-01 13:02 -0700
        Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-02 09:57 +1300
          Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-03 10:55 +1300
            Re: Worst Case Greedy Walk "INFINITY POWER" <infinity@limited.com> - 2011-11-03 09:39 +1000
              Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-07 17:09 +1300
                Re: Worst Case Greedy Walk "INFINITY POWER" <infinity@limited.com> - 2011-11-08 04:04 +1000
                Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-08 09:54 +1300
                Re: Worst Case Greedy Walk seeWebInstead@rem.intarweb.org (Robert Maas, http://tinyurl.com/uh3t) - 2011-11-13 11:50 -0800
                Re: Worst Case Greedy Walk "INFINITY POWER" <infinity@limited.com> - 2011-11-14 06:58 +1000
                Re: Worst Case Greedy Walk seeWebInstead@rem.intarweb.org (Robert Maas, http://tinyurl.com/uh3t) - 2012-03-29 00:28 -0700
                Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-08 11:44 +1300
                Re: Worst Case Greedy Walk mike fee <m.fee@irl.nospam.cri.nz> - 2011-11-08 14:28 +1300
    Re: Worst Case Greedy Walk Andrew Tomazos <andrew@tomazos.com> - 2011-11-01 12:46 -0700
      Re: Worst Case Greedy Walk "Chris Uppal" <chris.uppal@metagnostic.REMOVE-THIS.org> - 2011-11-02 08:16 +0000
        Re: Worst Case Greedy Walk Patricia Shanahan <pats@acm.org> - 2011-11-02 05:27 -0700
  Re: Worst Case Greedy Walk Graham Cooper <grahamcooper7@gmail.com> - 2011-11-01 14:29 -0700
    Re: Worst Case Greedy Walk Graham Cooper <grahamcooper7@gmail.com> - 2011-11-01 15:30 -0700
    Re: Worst Case Greedy Walk Steve Thompson <thomps2048@yahoo.ca> - 2011-11-01 20:56 -0400
  Re: Worst Case Greedy Walk quasi <quasi@null.set> - 2011-11-02 01:55 -0500
    Re: Worst Case Greedy Walk quasi <quasi@null.set> - 2011-11-02 18:24 -0500
  Re: Worst Case Greedy Walk "INFINITY POWER" <infinity@limited.com> - 2011-11-02 17:49 +1000

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