SUBSET_SUM_SERIAL
Solve a Subset Sum Problem by Exhaustive Search

SUBSET_SUM_SERIAL is a FORTRAN77 library which illustrates how a subset sum problem can be solved by exhaustive search.

We are given a collection of (21) weights and a target value (24639098). We seek a combination of the weights which adds up to the target value.

The function subset_sum_serial.m simply considers every possible subset of the weights, determines its sum, and compares that to the target value. The first case in which the target value is matched is returned as the solution.

This program, which solves the problem serially, is primarily intended to be a starting point for a parallel programming approach.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SUBSET_SUM_SERIAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BT_SERIAL, a FORTRAN77 program which runs the serial version of the NAS Parallel Benchmark known as "BT" (block tridiagonal solver for 3D PDE).

CG_SERIAL, a FORTRAN77 program which a serial version of the Conjugate Gradient (CG) NAS Parallel Benchmark.

EP_SERIAL, a FORTRAN77 program which runs the serial version of the NAS Parallel Benchmark known as "EP" (embarassingly parallel).

FFT_SERIAL, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for developing a parallel version using OpenMP.

FIRE_SERIAL, a FORTRAN77 program which simulates a forest fire over a rectangular array of trees, starting at a single random location. It is intended as a starting point for the development of a parallel version.

HEATED_PLATE, a FORTRAN77 program which solves the steady state heat equation in a 2D rectangular region, and is intended as a starting point for implementing an OpenMP parallel version.

MD, a FORTRAN77 program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing an OpenMP parallel version.

MXM_SERIAL, a FORTRAN77 program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.

POISSON_SERIAL, a FORTRAN77 program which computes an approximate solution to the Poisson equation in a rectangle, and is intended as the starting point for the creation of a parallel version.

PRIME_SERIAL, a FORTRAN77 program which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.

QUAD_SERIAL, a FORTRAN77 program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.

QUAD2D_SERIAL, a FORTRAN77 program which approximates an integral over a 2D region using a product quadrature rule, and is intended as a starting point for parallelization exercises.

SEARCH_SERIAL, a FORTRAN77 program which searches the integers from A to B for a value J such that F(J) = C. this version of the program is intended as a starting point for a parallel approach.

SUBSET_SUM, a FORTRAN77 library which seeks solutions of the subset sum problem.

Reference:

• Silvano Martello, Paolo Toth,
  Knapsack Problems: Algorithms and Computer Implementations,
  Wiley, 1990,
  ISBN: 0-471-92420-2,
  LC: QA267.7.M37.

Source Code:

• subset_sum_serial.f, the source code.
• subset_sum_serial.sh, BASH commands to compile the source code.

Examples and Tests:

• subset_sum_serial_prb.f, a sample calling program.
• subset_sum_serial_prb.sh, BASH commands to compile and run the sample program.
• subset_sum_serial_prb_output.txt, the output file.

List of Routines:

• I4_TO_DIGITS_BINARY produces the binary digits of an I4.
• SUBSET_SUM_SERIAL seeks a subset of a set that has a given sum.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.