PCbO: Parallel CbO


pcbo - computes formal concepts and maximal frequent itemsets




This program computes intents of all formal concepts in an object-attribute data set (a formal context), i.e. the algorithm computes all maximal submatrices of a boolean matrix which are full of 1's. The program implements PCbO, a parallel algorithm based on Kuznetsov's CbO.

The INPUT-FILE is in the usual FIMI format: each line represents a transaction or an object and it contains of a list of attributes/features/items. If the INPUT-FILE is omitted or if it equals to `-', the program reads the input form the stdin. The OUTPUT-FILE has a similar format, each line represents one intent (itemset), where numbers indicate attributes in the intent (itemset). If the OUTPUT-FILE is omitted or if it equals to `-', the program writes the input to the stdout.

Optional arguments

sets the initial index of the first attribute. The default value is 0, meaning that attributes are numbered from 0 upwards. If a data set uses attributes numbered from 1, you should use the `-1' switch, and so on.
sets the number of threads to cpus. The default value is 1, meaning that pcbo runs in the single-threaded version. In order to benefit from the parallel computation, you have to set cpus to at least 2. The recommended values is the number of hardware processors (processor cores) in your system or higher (typically, two or three times the number of all CPU cores).
sets the initial stage recursion level to depth. The value influences the number of formal concepts which are computed during the initial sequential stage. Namely, the algorithm first computes all concepts which are derivable in less than depth steps. The default value is 3. A reasonable choice of the value is 3 or 4. In general, higher values may lead to a more uniform distribution of concepts over the separate threads. On the other hand, too large values of depth degrade the parallel computation into the serial one. Some experimentation to achieve the best results is necessary. Anyway, a good starting value seems to be 3 or 4.
the minimal support considered is set to min-support. The default value is 0, meaning that the support is disregarded and all intents (itemsets) are written to the output. If min-support is set to a positive value, only itemsets having extents with at least min-support are written to the output.
sets the verbosity level to a specified value. Permitted values are numbers from 0 up to 3. The default value is 1. Verbosity level 0 (no output) just computes the intents and produces no output. Verbosity level 1 produces lists of intents with no auxiliary output. Verbosity levels 2 and higher write additional information to stderr.


pcbo -1 mushroom.dat

Computes all intents in the file named mushroom.dat where 1 denotes the first attribute in mushroom.dat. The output is written to the standard output.

pcbo -1 -P6 mushroom.dat

Computes all intents in mushroom.dat with first attribute 1 using 6 threads. The output is written to the standard output.

pcbo -P8 -L4 foo.dat output-intents.dat

Computes all intents in mushroom.dat with 8 threads using the initial stage recursion depth 4, and writing results to output-intents.dat.

pcbo -P4 -L3 -V2 - output.dat

Computes all intents in data from the standard input with 4 threads using the initial stage recursion depth 3, and verbosity level 2, writing result to output.dat.


Written by Petr Krajca, Jan Outrata, and Vilem Vychodil.


Report bugs to <fcalgs-bugs@lists.sourceforge.net>.


GNU GPL 2 (http://www.gnu.org/licenses/gpl-2.0.html). This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.

Users in academia are kindly asked to cite the following resources if the software is used to pursue any research activities which may result in publications:

Krajca P., Outrata J., Vychodil V.: Parallel Recursive Algorithm for FCA. In: Proc. CLA 2008, CEUR WS, 433(2008), 71-82.


The program can be obtained from http://fcalgs.sourceforge.net


Preliminary version of PCbO is described in the aforementioned paper that can be downloaded from


Further information can be found at http://fcalgs.sourceforge.net