SATISFY_OPENMP is a FORTRAN90 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 | 4.38 seconds |
2 | 8,388,608 | 2.29 seconds |
4 | 8,388,608 | 2.29 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 FORTRAN90 version.
DIJKSTRA_OPENMP, a FORTRAN90 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.
FFT_OPENMP, a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.
HEATED_PLATE_OPENMP, a FORTRAN90 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.
HELLO_OPENMP, a FORTRAN90 program which prints out "Hello, world!" using the OpenMP parallel programming environment.
JACOBI_OPENMP, a FORTRAN90 program which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.
MANDELBROT_OPENMP, a FORTRAN90 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.
MD_OPENMP, a FORTRAN90 program which carries out a molecular dynamics simulation using OpenMP.
MULTITASK_OPENMP, a FORTRAN90 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.
MXM_OPENMP, a FORTRAN90 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.
OPENMP_RCC, FORTRAN90 programs which illustrate how a FORTRAN90 program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).
POISSON_OPENMP, a FORTRAN90 program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.
PRIME_OPENMP, a FORTRAN90 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.
QUAD_OPENMP, a FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.
RANDOM_OPENMP, a FORTRAN90 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
SATISFY, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfy problem.
SATISFY_MPI, a FORTRAN90 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 FORTRAN90 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.
SGEFA_OPENMP, a FORTRAN90 program which solves a linear system by Gaussian elimination, using OpenMP.
ZIGGURAT_OPENMP, a FORTRAN90 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.
You can go up one level to the FORTRAN90 source codes.