######################################################################
Algorithm::Bucketizer 0.09
######################################################################
NAME
Algorithm::Bucketizer - Distribute sized items to buckets with limited
size
SYNOPSIS
use Algorithm::Bucketizer;
# Create a bucketizer
my $bucketizer = Algorithm::Bucketizer->new(bucketsize => $size);
# Add items to it
$bucketizer->add_item($item, $size);
# Optimize distribution
$bucketizer->optimize(maxrounds => 100);
# When done adding, get the buckets
# (they're of type Algorithm::Bucketizer::Bucket)
my @buckets = $bucketizer->buckets();
# Access bucket content by using
# Algorithm::Bucketizer::Bucket methods
my @items = $bucket->items();
my $serial = $bucket->serial();
DESCRIPTION
So, you own a number of mp3-Songs on your hard disc and want to copy
them to a number of CDs, maxing out the space available on each of them?
You want to distribute your picture collection into several folders, so
each of them doesn't exceed a certain size? "Algorithm::Bucketizer"
comes to the rescue.
"Algorithm::Bucketizer" distributes items of a defined size into a
number of dynamically created buckets, each of them capable of holding
items of a defined total size.
By calling the "$bucketizer->add_item()" method with the item (can be a
scalar or an object reference) and its size as parameters, you're adding
items to the system. The bucketizer will determine if the item fits into
one of the existing buckets and put it in there if possible. If none of
the existing buckets has enough space left to hold the new item (or if
no buckets exist yet for that matter), the bucketizer will create a new
bucket and put the item in there.
After adding all items to the system, the bucketizer lets you iterate
over all buckets with the "$bucketizer->items()" method and determine
what's in each of them.
Algorithms
Currently, "Algorithm::Bucketizer" comes with two algorithms, "simple"
and "retry".
In "simple" mode, the algorithm will just try to fit in your items in
the order in which they're arriving. If an item fits into the current
bucket, it's being dropped in, if not, the algorithm moves on to the
next bucket. It never goes back to previous buckets, although a new item
might as well fit in there. This mode might be useful if preserving the
original order of items is required.
In "retry" mode, the algorithm will try each existing bucket first,
before opening a new one. If you have many items of various sizes,
"retry" allows you to fit them into less buckets than in "simple" mode.
The "new()" method chooses the algorithm:
my $dumb = Algorithm::Bucketizer->new( algorithm => "simple" );
my $smart = Algorithm::Bucketizer->new( algorithm => "retry" );
In addition to these inserting algorithms, check "Optimize" to optimize
the distribution, minimizing the number of required buckets.
Prefilling Buckets
Sometimes you will have preexisting buckets, which you need to tell the
algorithm about before it starts adding new items. The
"prefill_bucket()" method does exactly that, simply putting an item into
a specified bucket:
$b->prefill_bucket($bucket_idx, $item, $itemsize);
$bucket_idx is the index of the bucket, starting from 0. Non-existing
buckets are automatically created for you. Make sure you have a
consecutive number of buckets at the end of the prefill.
Optimize
Once you've inserted all items, you might choose to optimize the
distribution over the buckets, in order to *minimize* the number of
required buckets to hold all the elements.
Optimally distributing a number discrete-sized items into a number of
discrete-sized buckets, however, is a non-trivial task. It's the
"bin-packing problem", related to the "knapsack problem", which are both
*NP-complete*.
"Algorithm::Bucketize" therefore provides different optimization
techniques to (stupidly) approximate an ideal solution, which can't be
obtained otherwise (yet).
Currently, it implements "random" and "brute_force".
"random" tries to randomly vary the distribution until a time or round
limit is reached.
# Try randomly to improve distribution,
# timing out after 100 rounds
$b->optimize(algorithm => "random", maxrounds => 100);
# Try randomly to improve distribution,
# timing out after 60 secs
$b->optimize(algorithm => "random", maxtime => 60);
# Try to improve distribution by brute_force trying
# all possible combinations (watch out: can take forever)
$b->optimize(algorithm => "brute_force",
maxtime => ...,
maxrounds => ...,
);
I'm currently evaluating more sophisticated methods suggested by more
mathematically inclined people :).
FUNCTIONS
*
my $b = Algorithm::Bucketizer->new(
bucketsize => $size,
algorithm => $algorithm
);
Creates a new "Algorithm::Bucketizer" object and returns a reference
to it.
The "bucketsize" name-value pair is somewhat mandatory, because you
want to set the size of your buckets, otherwise they will default to
100, which isn't what you want in most cases.
"algorithm" can be left out, it defaults to "simple". If you want
retry behaviour, specify "retry" (see "Algorithms").
*
$b->add_item($item_name, $item_size);
Adds an item with the specified name and size to the next available
bucket, according to the chosen algorithm. If you want to place an
item into a specific bucket (e.g. in order to prefill buckets), use
"prefill_bucket()" instead, which is described below.
Returns 1 on sucess and "undef" if something goes badly wrong (e.g.
the bucket size is smaller than the item, i.e. there's no way it's
ever going to fit in *any* bucket).
*
my @buckets = $b->buckets();
Return a list of buckets. The list contains elements of type
"Algorithm::Bucketizer::Bucket", which understand the following
methods:
*
my @items = $bucket->items();
Returns a list of names of items in the bucket. Returns an empty
list if the bucket is empty.
*
my $level = $bucket->level();
Return how full the bucket is. That's the size of all items in
the bucket combined.
*
my $bucket_index = $bucket->idx();
Return the bucket's index. The first bucket has index 0.
*
my $serial_number = $bucket->serial();
Return the bucket serial number. That's the bucket index plus 1.
*
$b->optimize(
algorithm => $algorithm,
maxtime => $seconds,
maxrounds => $number_of_rounds
);
Optimize bucket distribution. Currently "random" and "brute_force"
are implemented. Both can be ("random" *must* be) terminated by
either the maximum number of seconds ("maxtime") or iterations
("maxrounds").
EXAMPLE
We've got buckets which hold a weight of 100 each, and we've got 10
items weighing 30, 31, 32, ... 39. Distribute them into buckets.
use Algorithm::Bucketizer;
my $b = Algorithm::Bucketizer->new( bucketsize => 100 );
for my $i (1..10) {
$b->add_item($i, 30+$i);
}
for my $bucket ($b->buckets()) {
for my $item ($bucket->items()) {
print "Bucket ", $bucket->serial(), ": Item $item\n";
}
print "\n";
}
Output:
Bucket 1: Item 1
Bucket 1: Item 2
Bucket 1: Item 3
Bucket 2: Item 4
Bucket 2: Item 5
Bucket 3: Item 6
Bucket 3: Item 7
Bucket 4: Item 8
Bucket 4: Item 9
Bucket 5: Item 10
REQUIRES
Algorithm::Permute 0.04 if you want to use the "brute_force" method.
AUTHOR
Mike Schilli,
COPYRIGHT AND LICENSE
Copyright 2002 by Mike Schilli
This library is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.