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ALGORITHMS.t2t
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| [Home index.html] | [CHM chm.html] | [BMZ bmz.html] | [BRZ Algorithm brz.html] | [FCH Algorithm fch.html]
| [Home index.html] | [BDZ bdz.html] | [BMZ bmz.html] | [CHM chm.html] | [BRZ brz.html] | [FCH fch.html]
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BMZ Algorithm
%!includeconf: CONFIG.t2t
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==History==
At the end of 2003, professor [Nivio Ziviani http://www.dcc.ufmg.br/~nivio] was
finishing the second edition of his [book http://www.dcc.ufmg.br/algoritmos/].
During the [book http://www.dcc.ufmg.br/algoritmos/] writing,
professor [Nivio Ziviani http://www.dcc.ufmg.br/~nivio] studied the problem of generating
[minimal perfect hash functions concepts.html]
(if you are not familiarized with this problem, see [[1 #papers]][[2 #papers]]).
Professor [Nivio Ziviani http://www.dcc.ufmg.br/~nivio] coded a modified version of
the [CHM algorithm chm.html], which was proposed by
Czech, Havas and Majewski, and put it in his [book http://www.dcc.ufmg.br/algoritmos/].
The [CHM algorithm chm.html] is based on acyclic random graphs to generate
[order preserving minimal perfect hash functions concepts.html] in linear time.
Professor [Nivio Ziviani http://www.dcc.ufmg.br/~nivio]
argued himself, why must the random graph
be acyclic? In the modified version availalbe in his [book http://www.dcc.ufmg.br/algoritmos/] he got rid of this restriction.
The modification presented a problem, it was impossible to generate minimal perfect hash functions
for sets with more than 1000 keys.
At the same time, [Fabiano C. Botelho http://www.dcc.ufmg.br/~fbotelho],
a master degree student at [Departament of Computer Science http://www.dcc.ufmg.br] in
[Federal University of Minas Gerais http://www.ufmg.br],
started to be advised by [Nivio Ziviani http://www.dcc.ufmg.br/~nivio] who presented the problem
to [Fabiano http://www.dcc.ufmg.br/~fbotelho].
During the master, [Fabiano http://www.dcc.ufmg.br/~fbotelho] and
[Nivio Ziviani http://www.dcc.ufmg.br/~nivio] faced lots of problems.
In april of 2004, [Fabiano http://www.dcc.ufmg.br/~fbotelho] was talking with a
friend of him (David Menoti) about the problems
and many ideas appeared.
The ideas were implemented and a very fast algorithm to generate
minimal perfect hash functions had been designed.
We refer the algorithm to as **BMZ**, because it was conceived by Fabiano C. **B**otelho,
David **M**enoti and Nivio **Z**iviani. The algorithm is described in [[1 #papers]].
To analyse BMZ algorithm we needed some results from the random graph theory, so
we invited professor [Yoshiharu Kohayakawa http://www.ime.usp.br/~yoshi] to help us.
The final description and analysis of BMZ algorithm is presented in [[2 #papers]].
----------------------------------------
==The Algorithm==
The BMZ algorithm shares several features with the [CHM algorithm chm.html].
In particular, BMZ algorithm is also
based on the generation of random graphs [figs/img27.png], where [figs/img28.png] is in
one-to-one correspondence with the key set [figs/img20.png] for which we wish to
generate a [minimal perfect hash function concepts.html].
The two main differences between BMZ algorithm and CHM algorithm
are as follows: (//i//) BMZ algorithm generates random
graphs [figs/img27.png] with [figs/img29.png] and [figs/img30.png], where [figs/img31.png],
and hence [figs/img32.png] necessarily contains cycles,
while CHM algorithm generates //acyclic// random
graphs [figs/img27.png] with [figs/img29.png] and [figs/img30.png],
with a greater number of vertices: [figs/img33.png];
(//ii//) CHM algorithm generates [order preserving minimal perfect hash functions concepts.html]
while BMZ algorithm does not preserve order. Thus, BMZ algorithm improves
the space requirement at the expense of generating functions that are not
order preserving.
Suppose [figs/img14.png] is a universe of //keys//.
Let [figs/img17.png] be a set of [figs/img8.png] keys from [figs/img14.png].
Let us show how the BMZ algorithm constructs a minimal perfect hash function [figs/img7.png].
We make use of two auxiliary random functions [figs/img41.png] and [figs/img55.png],
where [figs/img56.png] for some suitably chosen integer [figs/img57.png],
where [figs/img58.png].We build a random graph [figs/img59.png] on [figs/img60.png],
whose edge set is [figs/img61.png]. There is an edge in [figs/img32.png] for each
key in the set of keys [figs/img20.png].
In what follows, we shall be interested in the //2-core// of
the random graph [figs/img32.png], that is, the maximal subgraph
of [figs/img32.png] with minimal degree at
least 2 (see [[2 #papers]] for details).
Because of its importance in our context, we call the 2-core the
//critical// subgraph of [figs/img32.png] and denote it by [figs/img63.png].
The vertices and edges in [figs/img63.png] are said to be //critical//.
We let [figs/img64.png] and [figs/img65.png].
Moreover, we let [figs/img66.png] be the set of //non-critical//
vertices in [figs/img32.png].
We also let [figs/img67.png] be the set of all critical
vertices that have at least one non-critical vertex as a neighbour.
Let [figs/img68.png] be the set of //non-critical// edges in [figs/img32.png].
Finally, we let [figs/img69.png] be the //non-critical// subgraph
of [figs/img32.png].
The non-critical subgraph [figs/img70.png] corresponds to the //acyclic part//
of [figs/img32.png].
We have [figs/img71.png].
We then construct a suitable labelling [figs/img72.png] of the vertices
of [figs/img32.png]: we choose [figs/img73.png] for each [figs/img74.png] in such
a way that [figs/img75.png] ([figs/img18.png]) is a
minimal perfect hash function for [figs/img20.png].
This labelling [figs/img37.png] can be found in linear time
if the number of edges in [figs/img63.png] is at most [figs/img76.png] (see [[2 #papers]]
for details).
Figure 1 presents a pseudo code for the BMZ algorithm.
The procedure BMZ ([figs/img20.png], [figs/img37.png]) receives as input the set of
keys [figs/img20.png] and produces the labelling [figs/img37.png].
The method uses a mapping, ordering and searching approach.
We now describe each step.
| procedure BMZ ([figs/img20.png], [figs/img37.png])
|     Mapping ([figs/img20.png], [figs/img32.png]);
|     Ordering ([figs/img32.png], [figs/img63.png], [figs/img70.png]);
|     Searching ([figs/img32.png], [figs/img63.png], [figs/img70.png], [figs/img37.png]);
| **Figure 1**: Main steps of BMZ algorithm for constructing a minimal perfect hash function
----------------------------------------
===Mapping Step===
The procedure Mapping ([figs/img20.png], [figs/img32.png]) receives as input the set
of keys [figs/img20.png] and generates the random graph [figs/img59.png], by generating
two auxiliary functions [figs/img41.png], [figs/img78.png].
The functions [figs/img41.png] and [figs/img42.png] are constructed as follows.
We impose some upper bound [figs/img79.png] on the lengths of the keys in [figs/img20.png].
To define [figs/img80.png] ([figs/img81.png], [figs/img62.png]), we generate
an [figs/img82.png] table of random integers [figs/img83.png].
For a key [figs/img18.png] of length [figs/img84.png] and [figs/img85.png], we let
| [figs/img86.png]
The random graph [figs/img59.png] has vertex set [figs/img56.png] and
edge set [figs/img61.png]. We need [figs/img32.png] to be
simple, i.e., [figs/img32.png] should have neither loops nor multiple edges.
A loop occurs when [figs/img87.png] for some [figs/img18.png].
We solve this in an ad hoc manner: we simply let [figs/img88.png] in this case.
If we still find a loop after this, we generate another pair [figs/img89.png].
When a multiple edge occurs we abort and generate a new pair [figs/img89.png].
Although the function above causes [collisions concepts.html] with probability //1/t//,
in [cmph library index.html] we use faster hash
functions ([DJB2 hash http://www.cs.yorku.ca/~oz/hash.html], [FNV hash http://www.isthe.com/chongo/tech/comp/fnv/],
[Jenkins hash http://burtleburtle.net/bob/hash/doobs.html] and [SDBM hash http://www.cs.yorku.ca/~oz/hash.html])
in which we do not need to impose any upper bound [figs/img79.png] on the lengths of the keys in [figs/img20.png].
As mentioned before, for us to find the labelling [figs/img72.png] of the
vertices of [figs/img59.png] in linear time,
we require that [figs/img108.png].
The crucial step now is to determine the value
of [figs/img1.png] (in [figs/img57.png]) to obtain a random
graph [figs/img71.png] with [figs/img109.png].
Botelho, Menoti an Ziviani determinded emprically in [[1 #papers]] that
the value of [figs/img1.png] is //1.15//. This value is remarkably
close to the theoretical value determined in [[2 #papers]],
which is around [figs/img112.png].
----------------------------------------
===Ordering Step===
The procedure Ordering ([figs/img32.png], [figs/img63.png], [figs/img70.png]) receives
as input the graph [figs/img32.png] and partitions [figs/img32.png] into the two
subgraphs [figs/img63.png] and [figs/img70.png], so that [figs/img71.png].
Figure 2 presents a sample graph with 9 vertices
and 8 edges, where the degree of a vertex is shown besides each vertex.
Initially, all vertices with degree 1 are added to a queue [figs/img136.png].
For the example shown in Figure 2(a), [figs/img137.png] after the initialization step.
| [figs/img138.png]
| **Figure 2:** Ordering step for a graph with 9 vertices and 8 edges.
Next, we remove one vertex [figs/img139.png] from the queue, decrement its degree and
the degree of the vertices with degree greater than 0 in the adjacent
list of [figs/img139.png], as depicted in Figure 2(b) for [figs/img140.png].
At this point, the adjacencies of [figs/img139.png] with degree 1 are
inserted into the queue, such as vertex 1.
This process is repeated until the queue becomes empty.
All vertices with degree 0 are non-critical vertices and the others are
critical vertices, as depicted in Figure 2(c).
Finally, to determine the vertices in [figs/img141.png] we collect all
vertices [figs/img142.png] with at least one vertex [figs/img143.png] that
is in Adj[figs/img144.png] and in [figs/img145.png], as the vertex 8 in Figure 2(c).
----------------------------------------
===Searching Step===
In the searching step, the key part is
the //perfect assignment problem//: find [figs/img153.png] such that
the function [figs/img154.png] defined by
| [figs/img155.png]
is a bijection from [figs/img156.png] to [figs/img157.png] (recall [figs/img158.png]).
We are interested in a labelling [figs/img72.png] of
the vertices of the graph [figs/img59.png] with
the property that if [figs/img11.png] and [figs/img22.png] are keys
in [figs/img20.png], then [figs/img159.png]; that is, if we associate
to each edge the sum of the labels on its endpoints, then these values
should be all distinct.
Moreover, we require that all the sums [figs/img160.png] ([figs/img18.png])
fall between [figs/img115.png] and [figs/img161.png], and thus we have a bijection
between [figs/img20.png] and [figs/img157.png].
The procedure Searching ([figs/img32.png], [figs/img63.png], [figs/img70.png], [figs/img37.png])
receives as input [figs/img32.png], [figs/img63.png], [figs/img70.png] and finds a
suitable [figs/img162.png] bit value for each vertex [figs/img74.png], stored in the
array [figs/img37.png].
This step is first performed for the vertices in the
critical subgraph [figs/img63.png] of [figs/img32.png] (the 2-core of [figs/img32.png])
and then it is performed for the vertices in [figs/img70.png] (the non-critical subgraph
of [figs/img32.png] that contains the "acyclic part" of [figs/img32.png]).
The reason the assignment of the [figs/img37.png] values is first
performed on the vertices in [figs/img63.png] is to resolve reassignments
as early as possible (such reassignments are consequences of the cycles
in [figs/img63.png] and are depicted hereinafter).
----------------------------------------
====Assignment of Values to Critical Vertices====
The labels [figs/img73.png] ([figs/img142.png])
are assigned in increasing order following a greedy
strategy where the critical vertices [figs/img139.png] are considered one at a time,
according to a breadth-first search on [figs/img63.png].
If a candidate value [figs/img11.png] for [figs/img73.png] is forbidden
because setting [figs/img163.png] would create two edges with the same sum,
we try [figs/img164.png] for [figs/img73.png]. This fact is referred to
as a //reassignment//.
Let [figs/img165.png] be the set of addresses assigned to edges in [figs/img166.png].
Initially [figs/img167.png].
Let [figs/img11.png] be a candidate value for [figs/img73.png].
Initially [figs/img168.png].
Considering the subgraph [figs/img63.png] in Figure 2(c),
a step by step example of the assignment of values to vertices in [figs/img63.png] is
presented in Figure 3.
Initially, a vertex [figs/img139.png] is chosen, the assignment [figs/img163.png] is made
and [figs/img11.png] is set to [figs/img164.png].
For example, suppose that vertex [figs/img169.png] in Figure 3(a) is
chosen, the assignment [figs/img170.png] is made and [figs/img11.png] is set to [figs/img96.png].
| [figs/img171.png]
| **Figure 3:** Example of the assignment of values to critical vertices.
In Figure 3(b), following the adjacent list of vertex [figs/img169.png],
the unassigned vertex [figs/img115.png] is reached.
At this point, we collect in the temporary variable [figs/img172.png] all adjacencies
of vertex [figs/img115.png] that have been assigned an [figs/img11.png] value,
and [figs/img173.png].
Next, for all [figs/img174.png], we check if [figs/img175.png].
Since [figs/img176.png], then [figs/img177.png] is set
to [figs/img96.png], [figs/img11.png] is incremented
by 1 (now [figs/img178.png]) and [figs/img179.png].
Next, vertex [figs/img180.png] is reached, [figs/img181.png] is set
to [figs/img62.png], [figs/img11.png] is set to [figs/img180.png] and [figs/img182.png].
Next, vertex [figs/img183.png] is reached and [figs/img184.png].
Since [figs/img185.png] and [figs/img186.png], then [figs/img187.png] is
set to [figs/img180.png], [figs/img11.png] is set to [figs/img183.png] and [figs/img188.png].
Finally, vertex [figs/img189.png] is reached and [figs/img190.png].
Since [figs/img191.png], [figs/img11.png] is incremented by 1 and set to 5, as depicted in
Figure 3(c).
Since [figs/img192.png], [figs/img11.png] is again incremented by 1 and set to 6,
as depicted in Figure 3(d).
These two reassignments are indicated by the arrows in Figure 3.
Since [figs/img193.png] and [figs/img194.png], then [figs/img195.png] is set
to [figs/img196.png] and [figs/img197.png]. This finishes the algorithm.
----------------------------------------
====Assignment of Values to Non-Critical Vertices====
As [figs/img70.png] is acyclic, we can impose the order in which addresses are
associated with edges in [figs/img70.png], making this step simple to solve
by a standard depth first search algorithm.
Therefore, in the assignment of values to vertices in [figs/img70.png] we
benefit from the unused addresses in the gaps left by the assignment of values
to vertices in [figs/img63.png].
For that, we start the depth-first search from the vertices in [figs/img141.png] because
the [figs/img37.png] values for these critical vertices were already assigned
and cannot be changed.
Considering the subgraph [figs/img70.png] in Figure 2(c),
a step by step example of the assignment of values to vertices in [figs/img70.png] is
presented in Figure 4.
Figure 4(a) presents the initial state of the algorithm.
The critical vertex 8 is the only one that has non-critical vertices as
adjacent.
In the example presented in Figure 3, the addresses [figs/img198.png] were not used.
So, taking the first unused address [figs/img115.png] and the vertex [figs/img96.png],
which is reached from the vertex [figs/img169.png], [figs/img199.png] is set
to [figs/img200.png], as shown in Figure 4(b).
The only vertex that is reached from vertex [figs/img96.png] is vertex [figs/img62.png], so
taking the unused address [figs/img183.png] we set [figs/img201.png] to [figs/img202.png],
as shown in Figure 4(c).
This process is repeated until the UnAssignedAddresses list becomes empty.
| [figs/img203.png]
| **Figure 4:** Example of the assignment of values to non-critical vertices.
----------------------------------------
==The Heuristic==[heuristic]
We now present an heuristic for BMZ algorithm that
reduces the value of [figs/img1.png] to any given value between //1.15// and //0.93//.
This reduces the space requirement to store the resulting function
to any given value between [figs/img12.png] words and [figs/img13.png] words.
The heuristic reuses, when possible, the set
of [figs/img11.png] values that caused reassignments, just before
trying [figs/img164.png].
Decreasing the value of [figs/img1.png] leads to an increase in the number of
iterations to generate [figs/img32.png].
For example, for [figs/img244.png] and [figs/img6.png], the analytical expected number
of iterations are [figs/img245.png] and [figs/img246.png], respectively (see [[2 #papers]]
for details),
while for [figs/img128.png] the same value is around //2.13//.
----------------------------------------
==Memory Consumption==
Now we detail the memory consumption to generate and to store minimal perfect hash functions
using the BMZ algorithm. The structures responsible for memory consumption are in the
following:
- Graph:
+ **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 [figs/img139.png], we can discover the edges that
contain [figs/img139.png] following its list of edges,
which starts on first[[figs/img139.png]] and the next
edges are given by next[...first[[figs/img139.png]]...]. 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.
+ **critical vertices(critical_nodes vector)**: is a vector of //cn// bits,
where each bit indicates if a vertex is critical (1) or non-critical (0).
Therefore, the critical and non-critical vertices are represented in //cn/8// bytes.
+ **critical edges (used_edges vector)**: is a vector of //n// bits, where each
bit indicates if an edge is critical (1) or non-critical (0). Therefore, the
critical and non-critical edges are represented in //n/8// bytes.
- Other auxiliary structures
+ **queue**: is a queue of integer numbers used in the breadth-first search of the
assignment of values to critical vertices. There is an entry in the queue for
each two critical vertices. Let [figs/img110.png] be the expected number of critical
vertices. Therefore, the queue is stored in //4*0.5*[figs/img110.png]=2[figs/img110.png]//.
+ **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
//4cn// bytes.
Thus, the total memory consumption of BMZ algorithm for generating a minimal
perfect hash function (MPHF) is: //(8.25c + 16.125)n +2[figs/img110.png] + O(1)// bytes.
As the value of constant //c// may be 1.15 and 0.93 we have:
|| //c// | [figs/img110.png] | Memory consumption to generate a MPHF |
| 0.93 | //0.497n// | //24.80n + O(1)// |
| 1.15 | //0.401n// | //26.42n + O(1)// |
| **Table 1:** Memory consumption to generate a MPHF using the BMZ algorithm.
The values of [figs/img110.png] were calculated using Eq.(1) presented in [[2 #papers]].
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:
|| //c// | Memory consumption to store a MPHF |
| 0.93 | //3.72n// |
| 1.15 | //4.60n// |
| **Table 2:** Memory consumption to store a MPHF generated by the BMZ algorithm.
----------------------------------------
==Experimental Results==
[CHM x BMZ comparison.html]
----------------------------------------
==Papers==[papers]
+ [F. C. Botelho http://www.dcc.ufmg.br/~fbotelho], D. Menoti, [N. Ziviani http://www.dcc.ufmg.br/~nivio]. [A New algorithm for constructing minimal perfect hash functions papers/bmz_tr004_04.ps], Technical Report TR004/04, Department of Computer Science, Federal University of Minas Gerais, 2004.
+ [F. C. Botelho http://www.dcc.ufmg.br/~fbotelho], Y. Kohayakawa, and [N. Ziviani http://www.dcc.ufmg.br/~nivio]. [A Practical Minimal Perfect Hashing Method papers/wea05.pdf]. //4th International Workshop on efficient and Experimental Algorithms (WEA05),// Springer-Verlag Lecture Notes in Computer Science, vol. 3505, Santorini Island, Greece, May 2005, 488-500.
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NEWSLOG.t2t
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@ -3,6 +3,22 @@ News Log
%!includeconf: CONFIG.t2t
----------------------------------------
==News for version 0.8==
- [An algorithm to generate MPHFs that require around 2.62 bits per key to be stored bdz.html], which is referred to as BDZ algorithm. The algorithm is the fastest one available in the literature for sets that can be treated in internal memory.
- The hash functions djb2, fnv and sdbm were removed because they do not use random seeds and therefore are not useful for MPHFs algorithms.
- All reported bugs and suggestions have been corrected and included as well.
----------------------------------------
==News for version 0.7==
- Added man pages and a pkgconfig file.
----------------------------------------
==News for version 0.6==

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README.t2t
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@ -42,6 +42,13 @@ The CMPH Library encapsulates the newest and more efficient algorithms in an eas
==Supported Algorithms==
%html% - [BDZ Algorithm bdz.html].
%txt% - BDZ Algorithm.
The fastest algorithm to build MPHFs. It is based on random 3-graphs. A 3-graph is a
generalization of a graph where each edge connects 3 vertices instead of only 2. The
resulting functions are not order preserving and can be stored in only //(2 + x)cn//
bits, where //c// should be larger than or equal to //1.23// and //x// is a constant
larger than //0// (actually, x = 1/b and b is a parameter that should be larger 2).
%html% - [BMZ Algorithm bmz.html].
%txt% - BMZ Algorithm.
A very fast algorithm based on cyclic random graphs to construct minimal
@ -72,20 +79,17 @@ The CMPH Library encapsulates the newest and more efficient algorithms in an eas
----------------------------------------
==News for version 0.8==
- [An algorithm to generate MPHFs that require around 2.62 bits per key to be stored bdz.html], which is referred to as BDZ algorithm. The algorithm is the fastest one available in the literature for sets that can be treated in internal memory.
- The hash functions djb2, fnv and sdbm were removed because they do not use random seeds and therefore are not useful for MPHFs algorithms.
- All reported bugs and suggestions have been corrected and included as well.
==News for version 0.7==
- Added man pages and a pkgconfig file.
==News for version 0.6==
- [An algorithm to generate MPHFs that require less than 4 bits per key to be stored fch.html], which is referred to as FCH algorithm. The algorithm is only efficient for small sets.
- The FCH algorithm is integrated with [BRZ algorithm brz.html] so that you will be able to efficiently generate space-efficient MPHFs for sets in the order of billion keys.
- All reported bugs and suggestions have been corrected and included as well.
[Click here to see the news log newslog.html]
----------------------------------------
==Examples==
@ -198,11 +202,9 @@ Minimum perfect hashing tool
* chm
* brz
* fch
* bdz
-f hash function (may be used multiple times) - valid values are
* djb2
* fnv
* jenkins
* sdbm
-V print version number and exit
-v increase verbosity (may be used multiple times)
-k number of keys
@ -211,7 +213,13 @@ Minimum perfect hashing tool
-m minimum perfect hash function file
-M main memory availability (in MB)
-d temporary directory used in brz algorithm
-b parmeter of BRZ algorithm to make the maximal number of keys in a bucket lower than 256
-b the meaning of this parameter depends on the algorithm used.
If BRZ algorithm is selected in -a option, than it is used
to make the maximal number of keys in a bucket lower than 256.
In this case its value should be an integer in the range [64,175].
If BDZ algorithm is selected in option -a, than it is used to
determine the size of some precomputed rank information and
its value should be an integer in the range [3,10]
keysfile line separated file with keys
```

2
configure.ac
View File

@ -1,6 +1,6 @@
dnl Process this file with autoconf to produce a configure script.
AC_INIT(Makefile.am)
AM_INIT_AUTOMAKE(cmph, 0.7)
AM_INIT_AUTOMAKE(cmph, 0.8)
AM_CONFIG_HEADER(config.h)
dnl Checks for programs.

8
src/main.c
View File

@ -45,7 +45,13 @@ void usage_long(const char *prg)
fprintf(stderr, " -m\t minimum perfect hash function file \n");
fprintf(stderr, " -M\t main memory availability (in MB)\n");
fprintf(stderr, " -d\t temporary directory used in brz algorithm \n");
fprintf(stderr, " -b\t parmeter of BRZ algorithm to make the maximal number of keys in a bucket lower than 256\n");
fprintf(stderr, " -b\t the meaning of this parameter depends on the algorithm used.\n");
fprintf(stderr, " \t If BRZ algorithm is selected in -a option, than it is used\n");
fprintf(stderr, " \t to make the maximal number of keys in a bucket lower than 256.\n");
fprintf(stderr, " \t In this case its value should be an integer in the range [64,175].\n");
fprintf(stderr, " \t If BDZ algorithm is selected in option -a, than it is used to\n");
fprintf(stderr, " \t determine the size of some precomputed rank information and\n");
fprintf(stderr, " \t its value should be an integer in the range [3,10]\n");
fprintf(stderr, " keysfile\t line separated file with keys\n");
}