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<html>
<head>
<title>
SATISFY_OPENMP - Seek Binary Circuit Inputs that Output 1, Using OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SATISFY_OPENMP <br> Seek Binary Circuit Inputs that Output 1, Using OpenMP
</h1>
<hr>
<p>
<b>SATISFY_OPENMP</b>
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.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
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!
</p>
<p>
This problem is a natural candidate for parallel computation, since
the individual evaluations of the circuit are completely independent.
</p>
<p>
On an Apple PowerPC G5 with two processors, the following results were
observed:
<table border="1" align="center">
<tr>
<th>Threads</th><th>2^N</th><th>Time</th>
</tr>
<tr>
<td>1</td><td>8,388,608</td><td>3.22 seconds</td>
</tr>
<tr>
<td>2</td><td>8,388,608</td><td>1.66 seconds</td>
</tr>
<tr>
<td>4</td><td>8,388,608</td><td>1.81 seconds</td>
</tr>
</table>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
In the BASH shell, the program could be run with 2 threads using the commands:
<pre>
export OMP_NUM_THREADS=2
./satisfy_openmp
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SATISFY_OPENMP</b> is available in
<a href = "../../c_src/satisfy_openmp/satisfy_openmp.html">a C version</a> and
<a href = "../../cpp_src/satisfy_openmp/satisfy_openmp.html">a C++ version</a> and
<a href = "../../f77_src/satisfy_openmp/satisfy_openmp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/satisfy_openmp/satisfy_openmp.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/cnf/cnf.html">
CNF</a>,
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.
</p>
<p>
<a href = "../../cpp_src/combo/combo.html">
COMBO</a>,
a C++ library which
includes many combinatorial routines.
</p>
<p>
<a href = "../../cpp_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a C++ program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../c_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a C program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../cpp_src/heated_plate_openmp/heated_plate_openmp.html">
HEATED_PLATE_OPENMP</a>,
a C++ program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using OpenMP to run in parallel.
</p>
<p>
<a href = "../../cpp_src/hello_openmp/hello_openmp.html">
HELLO_OPENMP</a>,
a C++ program which
prints out "Hello, world!" using the OpenMP parallel programming environment.
</p>
<p>
<a href = "../../f_src/lau_np/lau_np.html">
LAU_NP</a>,
a FORTRAN90 library which
implements heuristic algorithms for various NP-hard combinatorial problems.
</p>
<p>
<a href = "../../cpp_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a C++ program which
carries out a molecular dynamics simulation using OpenMP.
<p>
<p>
<a href = "../../cpp_src/multitask_openmp/multitask_openmp.html">
MULTITASK_OPENMP</a>,
a C++ program which
demonstrates how to "multitask", that is, to execute several unrelated
and distinct tasks simultaneously, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../cpp_src/mxv_openmp/mxv_openmp.html">
MXM_OPENMP</a>,
a C++ program which
computes a dense matrix product C=A*B,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../cpp_src/mxv_openmp/mxv_openmp.html">
MXV_OPENMP</a>,
a C++ program which
compares the performance of plain vanilla Fortran and the FORTRAN90
intrinsic routine MATMUL, for the matrix multiplication problem
y=A*x, with and without parallelization by OpenMP.
<p>
<p>
<a href = "../../cpp_src/openmp/openmp.html">
OPENMP</a>,
C++ programs which
illustrate the use of the OpenMP application program interface
for carrying out parallel computations in a shared memory environment.
</p>
<p>
<a href = "../../cpp_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a C++ 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.
</p>
<p>
<a href = "../../cpp_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a C++ program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../cpp_src/quad_openmp/quad_openmp.html">
QUAD_OPENMP</a>,
a C++ program which
approximates an integral using a quadrature rule, and carries out the
computation in parallel using OpenMP.
</p>
<p>
<a href = "../../cpp_src/random_openmp/random_openmp.html">
RANDOM_OPENMP</a>,
a C++ program which
illustrates how a parallel program using OpenMP can generate multiple
distinct streams of random numbers.
</p>
<p>
<a href = "../../cpp_src/satisfy/satisfy.html">
SATISFY</a>,
a C++ program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfy problem.
</p>
<p>
<a href = "../../cpp_src/satisfy_mpi/satisfy_mpi.html">
SATISFY_MPI</a>,
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.
</p>
<p>
<a href = "../../m_src/satisfy_parfor/satisfy_parfor.html">
SATISFY_PARFOR</a>,
a MATLAB program which
is intended to be run in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../cpp_src/schedule_openmp/schedule_openmp.html">
SCHEDULE_OPENMP</a>,
a C++ program which
demonstrates the default, static, and dynamic methods of "scheduling"
loop iterations in OpenMP to avoid work imbalance.
<p>
<p>
<a href = "../../cpp_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a C++ program which
solves a linear system by Gaussian elimination, using OpenMP.
<p>
<p>
<a href = "../../cpp_src/subset/subset.html">
SUBSET</a>,
a C++ library which
enumerates combinations, partitions, subsets, index sets,
and other combinatorial objects.
</p>
<p>
<a href = "../../cpp_src/ziggurat_openmp/ziggurat_openmp.html">
ZIGGURAT_OPENMP</a>,
a C++ program which
demonstrates how the ZIGGURAT library can be used to generate random numbers
in an OpenMP parallel program.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Michael Quinn,<br>
Parallel Programming in C with MPI and OpenMP,<br>
McGraw-Hill, 2004,<br>
ISBN13: 978-0071232654,<br>
LC: QA76.73.C15.Q55.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "satisfy_openmp.cpp">satisfy_openmp.cpp</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>SATISFY_LOCAL</b> runs SATISFY_OPENMP locally.
<ul>
<li>
<a href = "satisfy_local.sh">satisfy_local.sh</a>,
commands to compile the program and run with 1, 2, 4, and 8 threads.
</li>
<li>
<a href = "satisfy_local_output.txt">satisfy_local_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>SATISFY_ITHACA</b> runs SATISFY_OPENMP through the batch system.
<ul>
<li>
<a href = "satisfy_ithaca.sh">satisfy_ithaca.sh</a>,
commands to compile the program and run with 1, 2, 4, and 8 threads.
</li>
<li>
<a href = "satisfy_ithaca_output.txt">satisfy_ithaca_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for SATISFY_OPENMP.
</li>
<li>
<b>BVEC_NEXT</b> generates the next binary vector.
</li>
<li>
<b>CIRCUIT_VALUE</b> returns the value of a circuit for a given input set.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 04 September 2009.
</i>
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