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<b><font face="Arial, Helvetica, sans-serif" size="4" color="#000000">(2) <font color="#FF0000">analysis of directory dynamic hashing</font>
<font color="#FF0000"> directory version</font>
<font color="#0033CC">time</font> -- retrieving any page requires only two disk accesses
<font color="#0033CC">space</font> -- a lot of wasted storage
<font color="#0033CC">space utilization</font> :
the ratio of the number of records stored in the table divided by
the total amount of space allocated ( 69%)
<i>L(k)</i> ~ the expected number of leaf nodes needed to hold k records
<i>L(k) = 1 </i> ~ the records all fit in a single page.
<i><font color="#FF0000"> k > the page size ?</font></i>
j keys in the left subtree (L( j ) ) and k - j in the right tree
( L(k - j ) ), each with a given probability:
<i><font color="#0033CC"> </font></i><font color="#0033CC"><font color="#000000"> <i><font color="#FF0000"> L(k) </font></i>= <img src="image/text8-c1.gif" width="108" height="72" align="middle"> {L( j ) + L ( k - j ) } = <img src="image/text8-c2.gif" width="116" height="72" align="middle"> L( j )</font></font>
Mendelson goes on to show that: L(k) ~ <img src="image/text8-c.gif" width="41" height="41" align="middle"> (p page size )
utilization = <img src="image/text8-c.gif" width="41" height="41" align="middle"> ~ ln2 ~ 0.69
<font color="#FF0000">overflow page</font> ( to avoid double the directory size)
<font color="#0033CC">*</font> An overflow causes the allocation of a new page. The pointer to
new page is stored in the main page, and new identifiers are stored
in the overflow page.
<font color="#0033CC">*</font>overflow page increase storage utilization, but at the expense of
increased retrieval time
<font color="#0033CC">overflow page</font> <i> <font color="#FF0000">p </font></i> records --> utilization <font color="#FF0000"><i>2p/3p ( 66% )</i></font>
<font color="#0033CC">overflow page</font> <i><font color="#FF0000">p/2 </font></i> records --> utilization <i><font color="#FF0000">3p/4p ( 75% )</font></i>
ideal size for the overflow page
Larson : from p to p/2
directory size ( n - the number of records )
Fagin : 2[log<img src="image/text8-c.gif" width="41" height="41" align="middle"> ]</font></b></pre>
<p><img src="image/text8-c3.gif" width="417" height="168"></p>
<p><font face="Arial, Helvetica, sans-serif" size="4" color="#000000"><b>Lomet
: in the directory scheme, we do not view pages as of a fixed size, but allow
them to grow. </b></font></p>
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