88 lines
3.4 KiB
Plaintext
88 lines
3.4 KiB
Plaintext
CHM Algorithm
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==The Algorithm==
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The algorithm is presented in [[1,2,3 #papers]].
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==Memory Consumption==
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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 CHM algorithm. The structures responsible for memory consumption are in the
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following:
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- Graph:
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+ **first**: is a vector that stores //cn// integer numbers, each one representing
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the first edge (index in the vector edges) in the list of
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edges of each vertex.
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The integer numbers are 4 bytes long. Therefore,
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the vector first is stored in //4cn// bytes.
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+ **edges**: is a vector to represent the edges of the graph. As each edge
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is compounded by a pair of vertices, each entry stores two integer numbers
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of 4 bytes that represent the vertices. As there are //n// edges, the
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vector edges is stored in //8n// bytes.
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+ **next**: given a vertex [figs/img139.png], we can discover the edges that
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contain [figs/img139.png] following its list of edges, which starts on
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first[[figs/img139.png]] and the next
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edges are given by next[...first[[figs/img139.png]]...]. Therefore,
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the vectors first and next represent
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the linked lists of edges of each vertex. As there are two vertices for each edge,
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when an edge is iserted in the graph, it must be inserted in the two linked lists
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of the vertices in its composition. Therefore, there are //2n// entries of integer
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numbers in the vector next, so it is stored in //4*2n = 8n// bytes.
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- Other auxiliary structures
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+ **visited**: is a vector of //cn// bits, where each bit indicates if the g value of
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a given vertex was already defined. Therefore, the vector visited is stored
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in //cn/8// bytes.
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+ **function //g//**: is represented by a vector of //cn// integer numbers.
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As each integer number is 4 bytes long, the function //g// is stored in
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//4cn// bytes.
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Thus, the total memory consumption of CHM algorithm for generating a minimal
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perfect hash function (MPHF) is: //(8.125c + 16)n + O(1)// bytes.
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As the value of constant //c// must be at least 2.09 we have:
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|| //c// | Memory consumption to generate a MPHF |
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| 2.09 | //33.00n + O(1)// |
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| **Table 1:** Memory consumption to generate a MPHF using the CHM algorithm.
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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 //g// function. Thus, we need //4cn// bytes.
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Again we have:
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|| //c// | Memory consumption to store a MPHF |
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| 2.09 | //8.36n// |
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| **Table 2:** Memory consumption to store a MPHF generated by the CHM algorithm.
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----------------------------------------
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==Experimental Results==
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[CHM x BMZ comparison.html]
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----------------------------------------
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==Papers==[papers]
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+ Z.J. Czech, G. Havas, and B.S. Majewski. [An optimal algorithm for generating minimal perfect hash functions. papers/chm92.pdf], Information Processing Letters, 43(5):257-264, 1992.
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+ Z.J. Czech, G. Havas, and B.S. Majewski. Fundamental study perfect hashing.
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Theoretical Computer Science, 182:1-143, 1997.
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+ B.S. Majewski, N.C. Wormald, G. Havas, and Z.J. Czech. A family of perfect hashing methods.
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The Computer Journal, 39(6):547--554, 1996.
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