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Re: Re: Sorting by geographical proximity / clumping groups of items based on X and Y

by vroom (His Eminence)
on Jul 18, 2002 at 12:37 UTC ( #182777=note: print w/replies, xml ) Need Help??


in reply to Re: Sorting by geographical proximity / clumping groups of items based on X and Y
in thread Sorting by geographical proximity / clumping groups of items based on X and Y

I would say the most likely definition would be that all items within a clump are at most X feet from any other item in the clump. X would probably have a default of 300 feet or so but could be user-definable.
  • Comment on Re: Re: Sorting by geographical proximity / clumping groups of items based on X and Y

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Re: Sorting by geographical proximity / clumping groups of items based on X and Y
by Abigail-II (Bishop) on Jul 18, 2002 at 13:10 UTC
    Despite what I just said about NP-completeness, the following algorithm might give a reasonable solution (certainly not optimal).
    1. Let C be the set of all complaints.
    2. For each complaint c in C find the set S(c) of all complaints d in C such that the distance between c and d is less than X (X is user defined).
    3. Find complaint e in C such that |S(e)| <= |S(f)| for all f in C; that is, find the complaint who has the most other complaints nearby. Pick a random one in case of a tie.
    4. Make a clump out of e and S(e).
    5. Remove all complaints g in S(e) from C. For all h remaining in C, remove from S(h) all g in S(e).
    6. If C is empty, we're done. Else, goto 3.
    Some pseudo code:
    # Get set of all complaints. my @C = get_all_complaints; # Find all the associated sets. my %D = map {my $c = $_; $c => {map {$_ => 1} grep {$c ne $_ && distance ($c, $_) < $X} @C}} @C; while (%D) { # Find complaint with the most nearby. my ($complaint, $size) = (undef, 0); while (my ($c, $set) = each %D) { ($complaint = $c, $size = keys %$set) if keys %$set > $size; } # Found largest, make a clump. make_clump ($complaint, @{$D {$complaint}}); # Delete largest from set. my $set = delete $D {$complaint}; # Delete associated set from set. delete @D {keys %$set}; # Delete associated set from associated sets. delete @{$_} {keys %$set} for values %D; }
    The performance will be quadratic, I'm afraid.

    Abigail

      Shouldn't step 3 in your algorithm description:
      |S(e)| <= |S(f)|
      read
      |S(e)| > |S(f)|
      ? (Not having been a Math major, of course, could lead me to misinterpret "|S(t)|", which here I'm interpreting as "the size of set t".)
      Anyway, I had intended to suggest an algorithm dealing with sorting based on the lengths of line segments, but I now realize that's probably not much use in this case (since vroom wants to find the clumps, not necessarily a point). And reading further down the page, I like Ntromda's idea, but I, like him/her, wouldn't know how to begin coding it (without thinking about it for a long while...).
Re: Sorting by geographical proximity / clumping groups of items based on X and Y
by Abigail-II (Bishop) on Jul 18, 2002 at 12:46 UTC
    But you need more than that, otherwise the "Put each complaint in its own clump" is still a solution. It's tempting to add the restriction that you want to minimize the number of clumps, but that smells very much to an NP-complete covering problem.

    Abigail

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