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Author image Mike Schilli
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Algorithm::Bucketizer - Distribute sized items to buckets with limited size


  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();


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.


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. To query/manipulate the bucket the Bucketizer will try to fit in the next item, use current_bucket_index() explained below.

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.


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 :).


  •     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").

    Another optional parameter, add_buckets specifies if the bucketizer is allowed to add new buckets to the end of the brigade as it sees fit. It defaults to 1. If set to 0, the bucketizer will operate with a limited number of buckets, usually defined by add_bucket calls.

  •     $b->add_item($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 the Algorithm::Bucketizer::Bucket object of the lucky bucket 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->add_bucket(
            maxsize => $maxsize

    Adds a new bucket to the end of the bucket brigade. This method is useful for building brigades with buckets of various sizes.

  •     $b->current_bucket_idx( $idx );

    Set/retrieve the index of the bucket that the simple algorithm will use first in order to try to insert the next item.

  •     $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).


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";


    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


Algorithm::Permute 0.04 if you want to use the "brute_force" method.


This distribution comes with a script bucketize which puts files into directory buckets with limited size. Run perldoc bucketize for details.


Mike Schilli, <m@perlmeister.com>


Copyright 2002-2007 by Mike Schilli

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.