Despite what I just said about NP-completeness, the following algorithm
might give a reasonable solution (certainly not optimal).
- Let C be the set of all complaints.
- 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).
- 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.
- Make a clump out of e and S(e).
- Remove all complaints g in S(e) from C. For all h remaining in C,
remove from S(h) all g in S(e).
- 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
| [reply] [d/l] |

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...).
| [reply] |

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 | [reply] |

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