PARTITION_PROBLEM
The Partition Problem

PARTITION_PROBLEM is a FORTRAN90 library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

Licensing:

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

Languages:

PARTITION_PROBLEM is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CHANGE_MAKING, a FORTRAN90 library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

COMBINATION_LOCK, a FORTRAN90 program which simulates the process of determining the secret combination of a lock.

COMBO, a FORTRAN90 library which includes many combinatorial routines.

KNAPSACK_01, a FORTRAN90 library which uses brute force to solve small versions of the 0/1 knapsack problem;

LAMP, a FORTRAN77 library which solves linear assignment and matching problems.

LAU_NP, a FORTRAN90 library which implements heuristic algorithms for various NP-hard combinatorial problems.

PARTITION_PROBLEM, a dataset directory which contains examples of the partition problem, in which a set of numbers is given, and it is desired to break the set into two subsets with equal sum.

SATISFY, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET, a FORTRAN90 library which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.

SUBSET_SUM, a FORTRAN90 library which seeks solutions of the subset sum problem.

SUBSET_SUM_TASKS, a MATLAB program which runs in parallel, seeking solutions of the subset sum problem. Instructions are available on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.

TSP_BRUTE, a FORTRAN90 program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

Reference:

1. Alexander Dewdney,
   The Turing Omnibus,
   Freeman, 1989,
   ISBN13: 9780716781547,
   LC: QA76.D45.
2. Brian Hayes,
   The Easiest Hard Problem,
   American Scientist,
   Volume 90, Number 2, March-April 2002, pages 113-117.
3. Silvano Martello, Paolo Toth,
   Knapsack Problems: Algorithms and Computer Implementations,
   Wiley, 1990,
   ISBN: 0-471-92420-2,
   LC: QA267.7.M37.

Source Code:

• partition_problem.f90, the source code.

Examples and Tests:

• partition_problem_test.f90, a sample calling program.
• partition_problem_test.txt, the output file.

List of Routines:

• PARTITION_BRUTE approaches the partition problem using brute force.
• PARTITION_COUNT counts the solutions to a partition problem.
• SUBSET_NEXT computes the subset lexicographic successor.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.