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<a href="CedarBackup2-module.html">Package CedarBackup2</a> ::
Module knapsack
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<h1 class="epydoc">Module knapsack</h1><p class="nomargin-top"><span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html">source code</a></span></p>
<p>Provides the implementation for various knapsack algorithms.</p>
<p>Knapsack algorithms are "fit" algorithms, used to take a set
of "things" and decide on the optimal way to fit them into some
container. The focus of this code is to fit files onto a disc, although
the interface (in terms of item, item size and capacity size, with no
units) is generic enough that it can be applied to items other than
files.</p>
<p>All of the algorithms implemented below assume that
"optimal" means "use up as much of the disc's capacity as
possible", but each produces slightly different results. For
instance, the best fit and first fit algorithms tend to include fewer
files than the worst fit and alternate fit algorithms, even if they use
the disc space more efficiently.</p>
<p>Usually, for a given set of circumstances, it will be obvious to a
human which algorithm is the right one to use, based on trade-offs
between number of files included and ideal space utilization. It's a
little more difficult to do this programmatically. For Cedar Backup's
purposes (i.e. trying to fit a small number of collect-directory tarfiles
onto a disc), worst-fit is probably the best choice if the goal is to
include as many of the collect directories as possible.</p>
<hr />
<div class="fields"> <p><strong>Author:</strong>
Kenneth J. Pronovici <pronovic@ieee.org>
</p>
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<td><span class="summary-sig"><a href="CedarBackup2.knapsack-module.html#firstFit" class="summary-sig-name">firstFit</a>(<span class="summary-sig-arg">items</span>,
<span class="summary-sig-arg">capacity</span>)</span><br />
Implements the first-fit knapsack algorithm.</td>
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<span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#firstFit">source code</a></span>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a href="CedarBackup2.knapsack-module.html#bestFit" class="summary-sig-name">bestFit</a>(<span class="summary-sig-arg">items</span>,
<span class="summary-sig-arg">capacity</span>)</span><br />
Implements the best-fit knapsack algorithm.</td>
<td align="right" valign="top">
<span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#bestFit">source code</a></span>
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<td><span class="summary-sig"><a href="CedarBackup2.knapsack-module.html#worstFit" class="summary-sig-name">worstFit</a>(<span class="summary-sig-arg">items</span>,
<span class="summary-sig-arg">capacity</span>)</span><br />
Implements the worst-fit knapsack algorithm.</td>
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<span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#worstFit">source code</a></span>
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<span class="summary-type"> </span>
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<td><span class="summary-sig"><a href="CedarBackup2.knapsack-module.html#alternateFit" class="summary-sig-name">alternateFit</a>(<span class="summary-sig-arg">items</span>,
<span class="summary-sig-arg">capacity</span>)</span><br />
Implements the alternate-fit knapsack algorithm.</td>
<td align="right" valign="top">
<span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#alternateFit">source code</a></span>
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<a name="__package__"></a><span class="summary-name">__package__</span> = <code title="None">None</code><br />
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<a name="firstFit"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">firstFit</span>(<span class="sig-arg">items</span>,
<span class="sig-arg">capacity</span>)</span>
</h3>
</td><td align="right" valign="top"
><span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#firstFit">source code</a></span>
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<p>Implements the first-fit knapsack algorithm.</p>
<p>The first-fit algorithm proceeds through an unsorted list of items
until running out of items or meeting capacity exactly. If capacity is
exceeded, the item that caused capacity to be exceeded is thrown away and
the next one is tried. This algorithm generally performs more poorly
than the other algorithms both in terms of capacity utilization and item
utilization, but can be as much as an order of magnitude faster on large
lists of items because it doesn't require any sorting.</p>
<p>The "size" values in the items and capacity arguments must
be comparable, but they are unitless from the perspective of this
function. Zero-sized items and capacity are considered degenerate cases.
If capacity is zero, no items fit, period, even if the items list
contains zero-sized items.</p>
<p>The dictionary is indexed by its key, and then includes its key. This
seems kind of strange on first glance. It works this way to facilitate
easy sorting of the list on key if needed.</p>
<p>The function assumes that the list of items may be used destructively,
if needed. This avoids the overhead of having the function make a copy
of the list, if this is not required. Callers should pass
<code>items.copy()</code> if they do not want their version of the list
modified.</p>
<p>The function returns a list of chosen items and the unitless amount of
capacity used by the items.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>items</code></strong> (dictionary, keyed on item, of <code>(item, size)</code> tuples,
item as string and size as integer) - Items to operate on</li>
<li><strong class="pname"><code>capacity</code></strong> (integer) - Capacity of container to fit to</li>
</ul></dd>
<dt>Returns:</dt>
<dd>Tuple <code>(items, used)</code> as described above</dd>
</dl>
</td></tr></table>
</div>
<a name="bestFit"></a>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">bestFit</span>(<span class="sig-arg">items</span>,
<span class="sig-arg">capacity</span>)</span>
</h3>
</td><td align="right" valign="top"
><span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#bestFit">source code</a></span>
</td>
</tr></table>
<p>Implements the best-fit knapsack algorithm.</p>
<p>The best-fit algorithm proceeds through a sorted list of items (sorted
from largest to smallest) until running out of items or meeting capacity
exactly. If capacity is exceeded, the item that caused capacity to be
exceeded is thrown away and the next one is tried. The algorithm
effectively includes the minimum number of items possible in its search
for optimal capacity utilization. For large lists of mixed-size items,
it's not ususual to see the algorithm achieve 100% capacity utilization
by including fewer than 1% of the items. Probably because it often has
to look at fewer of the items before completing, it tends to be a little
faster than the worst-fit or alternate-fit algorithms.</p>
<p>The "size" values in the items and capacity arguments must
be comparable, but they are unitless from the perspective of this
function. Zero-sized items and capacity are considered degenerate cases.
If capacity is zero, no items fit, period, even if the items list
contains zero-sized items.</p>
<p>The dictionary is indexed by its key, and then includes its key. This
seems kind of strange on first glance. It works this way to facilitate
easy sorting of the list on key if needed.</p>
<p>The function assumes that the list of items may be used destructively,
if needed. This avoids the overhead of having the function make a copy
of the list, if this is not required. Callers should pass
<code>items.copy()</code> if they do not want their version of the list
modified.</p>
<p>The function returns a list of chosen items and the unitless amount of
capacity used by the items.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>items</code></strong> (dictionary, keyed on item, of <code>(item, size)</code> tuples,
item as string and size as integer) - Items to operate on</li>
<li><strong class="pname"><code>capacity</code></strong> (integer) - Capacity of container to fit to</li>
</ul></dd>
<dt>Returns:</dt>
<dd>Tuple <code>(items, used)</code> as described above</dd>
</dl>
</td></tr></table>
</div>
<a name="worstFit"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">worstFit</span>(<span class="sig-arg">items</span>,
<span class="sig-arg">capacity</span>)</span>
</h3>
</td><td align="right" valign="top"
><span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#worstFit">source code</a></span>
</td>
</tr></table>
<p>Implements the worst-fit knapsack algorithm.</p>
<p>The worst-fit algorithm proceeds through an a sorted list of items
(sorted from smallest to largest) until running out of items or meeting
capacity exactly. If capacity is exceeded, the item that caused capacity
to be exceeded is thrown away and the next one is tried. The algorithm
effectively includes the maximum number of items possible in its search
for optimal capacity utilization. It tends to be somewhat slower than
either the best-fit or alternate-fit algorithm, probably because on
average it has to look at more items before completing.</p>
<p>The "size" values in the items and capacity arguments must
be comparable, but they are unitless from the perspective of this
function. Zero-sized items and capacity are considered degenerate cases.
If capacity is zero, no items fit, period, even if the items list
contains zero-sized items.</p>
<p>The dictionary is indexed by its key, and then includes its key. This
seems kind of strange on first glance. It works this way to facilitate
easy sorting of the list on key if needed.</p>
<p>The function assumes that the list of items may be used destructively,
if needed. This avoids the overhead of having the function make a copy
of the list, if this is not required. Callers should pass
<code>items.copy()</code> if they do not want their version of the list
modified.</p>
<p>The function returns a list of chosen items and the unitless amount of
capacity used by the items.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>items</code></strong> (dictionary, keyed on item, of <code>(item, size)</code> tuples,
item as string and size as integer) - Items to operate on</li>
<li><strong class="pname"><code>capacity</code></strong> (integer) - Capacity of container to fit to</li>
</ul></dd>
<dt>Returns:</dt>
<dd>Tuple <code>(items, used)</code> as described above</dd>
</dl>
</td></tr></table>
</div>
<a name="alternateFit"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">alternateFit</span>(<span class="sig-arg">items</span>,
<span class="sig-arg">capacity</span>)</span>
</h3>
</td><td align="right" valign="top"
><span class="codelink"><a href="CedarBackup2.knapsack-pysrc.html#alternateFit">source code</a></span>
</td>
</tr></table>
<p>Implements the alternate-fit knapsack algorithm.</p>
<p>This algorithm (which I'm calling "alternate-fit" as in
"alternate from one to the other") tries to balance small and
large items to achieve better end-of-disk performance. Instead of just
working one direction through a list, it alternately works from the start
and end of a sorted list (sorted from smallest to largest), throwing away
any item which causes capacity to be exceeded. The algorithm tends to be
slower than the best-fit and first-fit algorithms, and slightly faster
than the worst-fit algorithm, probably because of the number of items it
considers on average before completing. It often achieves slightly
better capacity utilization than the worst-fit algorithm, while including
slighly fewer items.</p>
<p>The "size" values in the items and capacity arguments must
be comparable, but they are unitless from the perspective of this
function. Zero-sized items and capacity are considered degenerate cases.
If capacity is zero, no items fit, period, even if the items list
contains zero-sized items.</p>
<p>The dictionary is indexed by its key, and then includes its key. This
seems kind of strange on first glance. It works this way to facilitate
easy sorting of the list on key if needed.</p>
<p>The function assumes that the list of items may be used destructively,
if needed. This avoids the overhead of having the function make a copy
of the list, if this is not required. Callers should pass
<code>items.copy()</code> if they do not want their version of the list
modified.</p>
<p>The function returns a list of chosen items and the unitless amount of
capacity used by the items.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>items</code></strong> (dictionary, keyed on item, of <code>(item, size)</code> tuples,
item as string and size as integer) - Items to operate on</li>
<li><strong class="pname"><code>capacity</code></strong> (integer) - Capacity of container to fit to</li>
</ul></dd>
<dt>Returns:</dt>
<dd>Tuple <code>(items, used)</code> as described above</dd>
</dl>
</td></tr></table>
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