111 lines
4.1 KiB
HTML
111 lines
4.1 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<HTML>
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<HEAD>
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<META NAME="generator" CONTENT="http://txt2tags.org">
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<LINK REL="stylesheet" TYPE="text/css" HREF="DOC.css">
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<TITLE>FCH Algorithm</TITLE>
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</HEAD><BODY BGCOLOR="white" TEXT="black">
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<CENTER>
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<H1>FCH Algorithm</H1>
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</CENTER>
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<HR NOSHADE SIZE=1>
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<H2>The Algorithm</H2>
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<P>
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The algorithm is presented in <A HREF="#papers">[1</A>].
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</P>
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<HR NOSHADE SIZE=1>
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<H2>Memory Consumption</H2>
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<P>
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Now we detail the memory consumption to generate and to store minimal perfect hash functions
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using the FCH algorithm. The structures responsible for memory consumption are in the
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following:
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</P>
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<UL>
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<LI>A vector containing all the <I>n</I> keys.
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<LI>Data structure to speed up the searching step:
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<OL>
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<LI><B>random_table</B>: is a vector used to remember currently empty slots in the hash table. It stores <I>n</I> 4 byte long integer numbers. This vector initially contains a random permutation of the <I>n</I> hash addresses. A pointer called filled_count is used to keep the invariant that any slots to the right side of filled_count (inclusive) are empty and any ones to the left are filled.
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<LI><B>hash_table</B>: Table used to check whether all the collisions were resolved. It has <I>n</I> entries of one byte.
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<LI><B>map_table</B>: For any unfilled slot <I>x</I> in hash_table, the map_table vector contains <I>n</I> 4 byte long pointers pointing at random_table such that random_table[map_table[x]] = x. Thus, given an empty slot x in the hash_table, we can locate its position in the random_table vector through map_table.
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<P></P>
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</OL>
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<LI>Other auxiliary structures
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<OL>
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<LI><B>sorted_indexes</B>: is a vector of <I>cn/(log(n) + 1)</I> 4 byte long pointers to indirectly keep the buckets sorted by decreasing order of their sizes.
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<P></P>
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<LI><B>function <I>g</I></B>: is represented by a vector of <I>cn/(log(n) + 1)</I> 4 byte long integer numbers, one for each bucket. It is used to spread all the keys in a given bucket into the hash table without collisions.
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</OL>
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</UL>
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<P>
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Thus, the total memory consumption of FCH algorithm for generating a minimal
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perfect hash function (MPHF) is: <I>O(n) + 9n + 8cn/(log(n) + 1)</I> bytes.
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The value of parameter <I>c</I> must be greater than or equal to 2.6.
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</P>
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<P>
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Now we present the memory consumption to store the resulting function.
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We only need to store the <I>g</I> function and a constant number of bytes for the seed of the hash functions used in the resulting MPHF. Thus, we need <I>cn/(log(n) + 1) + O(1)</I> bytes.
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</P>
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<HR NOSHADE SIZE=1>
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<A NAME="papers"></A>
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<H2>Papers</H2>
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<OL>
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<LI>E.A. Fox, Q.F. Chen, and L.S. Heath. <A HREF="papers/fch92.pdf">A faster algorithm for constructing minimal perfect hash functions.</A> In Proc. 15th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 266-273, 1992.
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</OL>
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<HR NOSHADE SIZE=1>
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<TABLE ALIGN="center" CELLPADDING="4">
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<TR>
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<TD><A HREF="index.html">Home</A></TD>
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<TD><A HREF="chd.html">CHD</A></TD>
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<TD><A HREF="bdz.html">BDZ</A></TD>
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<TD><A HREF="bmz.html">BMZ</A></TD>
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<TD><A HREF="chm.html">CHM</A></TD>
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<TD><A HREF="brz.html">BRZ</A></TD>
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<TD><A HREF="fch.html">FCH</A></TD>
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</TR>
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</TABLE>
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<HR NOSHADE SIZE=1>
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<P>
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Enjoy!
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</P>
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<P>
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<A HREF="mailto:davi@users.sourceforge.net">Davi de Castro Reis</A>
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</P>
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<P>
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<A HREF="mailto:db8192@users.sourceforge.net">Djamel Belazzougui</A>
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</P>
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<P>
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<A HREF="mailto:fc_botelho@users.sourceforge.net">Fabiano Cupertino Botelho</A>
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</P>
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<P>
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<A HREF="mailto:nivio@dcc.ufmg.br">Nivio Ziviani</A>
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</P>
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