SATISFY_OPENMP is a C++ program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using OpenMP for parallel execution.
This problem assumes that we are given a logical circuit of AND, OR and NOT gates, with N=23 binary inputs and a single output. We are to determine all inputs which produce a 1 as the output.
The general problem is NP complete, so there is no known polynomial-time algorithm to solve the general case. The natural way to search for solutions then is exhaustive search of all 2^N possible inputs.
In an interesting way, this is a very extreme and discrete version of the problem of maximizing a scalar function of multiple variables. The difference is that here we know that both the input and output only have the values 0 and 1, rather than a continuous range of real values!
This problem is a natural candidate for parallel computation, since the individual evaluations of the circuit are completely independent.
On an Apple PowerPC G5 with two processors, the following results were observed:
Threads | 2^N | Time |
---|---|---|
1 | 8,388,608 | 3.22 seconds |
2 | 8,388,608 | 1.66 seconds |
4 | 8,388,608 | 1.81 seconds |
In the BASH shell, the program could be run with 2 threads using the commands:
export OMP_NUM_THREADS=2 ./satisfy_openmp
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
SATISFY_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.
CNF, a data directory which describes the DIMACS CNF file format for defining instances of the satisfy problem in for boolean formulas in conjunctive normal form.
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FFT_OPENMP, a C program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.
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RANDOM_OPENMP, a C++ program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
SATISFY, a C++ program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem.
SATISFY_MPI, a C++ program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem, using MPI to carry out the calculation in parallel.
SATISFY_PARFOR, a MATLAB program which is intended to be run in parallel using MATLAB's "PARFOR" feature.
SCHEDULE_OPENMP, a C++ program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.
SGEFA_OPENMP, a C++ program which solves a linear system by Gaussian elimination, using OpenMP.
SUBSET, a C++ library which enumerates combinations, partitions, subsets, index sets, and other combinatorial objects.
ZIGGURAT_OPENMP, a C++ program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.
SATISFY_LOCAL runs SATISFY_OPENMP locally.
SATISFY_ITHACA runs SATISFY_OPENMP through the batch system.
You can go up one level to the C++ source codes.