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