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C++ solvers for Minimum Cost Flow Problems
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ReadMe for the MCFClass project, a set of C++ solvers for (Linear or Convex Quadratic Separable) Min Cost Flow Problem solvers under the same interface deriving from the base class MCFClass.

The aim of MCFClass is to provide an abstraction layer between practitioners who need to solve MCF problems within complex applications and developers of MCF software. The idea is to provide an interface which caters for all the needs that a practitioner can have, thereby allowing him/her to use whichever algorithm - among those that have an implementation conforming to this interface - without bothering with the details of the implementation, and to easily switch between different algorithms.

MCFClass defines and "exports" the types of "flows" (MCFClass::FNumber), "costs" (MCFClass::CNumber) and so on, together with a set of comparison operators (ETZ, GTZ, ...) which automatically detect whether or not the underlying types are integers or floats, inserting appropriate "epsilons" in the latter case and avoiding them (for speed) in the former; these things are sorted out at compile time without user intervention.

This release comprises:

  • docs/: HTML doxygen documentation, also available at

  • doxygen/: files to produce the documentation

  • the text of the "GNU Lesser General Public License", Version 3.0, under which most of this code is distributed (but not all of it, see RelaxIV below)

  • MCFClass/: definition of the base class

  • MCFClone/: implements a "fake" MCF solver that takes two "real" ones and does everything on both; useful for testing the solvers (either for correctness or for efficiency) when used within "complex" approaches

  • MCFCplex/: implements a MCF solver conforming to the MCFClass interface based on calls to the commercial (but now free for academic purposes) Cplex solver from IBM

  • MCFSimplex/: implements a MCF solver conforming to the MCFClass interface based on the primal and dual revised network simplex algorithm

  • OPTUtils/: contains the OPTUtils.h file with a few minor utility functions

  • this file

  • RelaxIV/: implements a MCF solver conforming to the MCFClass interface based on the RELAXIV code by D. Bertsekas and P. Tseng, as described in Bertsekas, Dimitri P., and Paul Tseng. "RELAX-IV: A faster version of the RELAX code for solving minimum cost flow problems." (1994), Report LIDS-P-2276, MIT.

    be aware that RelaxIV is distributed under a less permissive academic license than the rest of the code (see RelaxIV/academicl.txt for details), which only applies to researchers of noncommercial and academic institutions, e.g., universities; if the license does not apply to you, you must not download the source or delete it immediately

  • SPTree/: implements a MCF solver partly conforming to the MCFClass interface, in the sense that is is only able to solve MCF instances that are in fact Shortest Path Tree ones (that is, only one source node and no arc capacities), but then does so using SPT algorithms (both label-setting and label-correcting variants can be used) that are much faster than complete MCF ones

  • pyMCFSimplex-0.9/: a Python-Wrapper for the MCFSimplex solver by Johannes from the G#.Blog, check README.txt for details

  • test/: contains two example Main files to use the library. One solves a given MCF instance with any one MCF solver, which can be chosen by just changing two lines of code. The other compares the results of two solvers in order to verify that they agree. See the comments in both files for more details

There are two more complete solvers available under the MCFClass interface, namely CS2 and MCFZIB. These are, however, distributed under a more restrictive academic license, which has to be explicitly accepted before getting hold of the code. Request forms are available at

Build and install

You can either use CMake or plain makefiles to build the library, your choice.

Using CMake

  • Clone the project from the repository and navigate inside its main directory.

  • If you installed the requirements you should be fine. Configure the project with:

mkdir build
cd build
cmake ..
  • You can now build the library:
  • Optionally, you can install the library with:
sudo make install
  • After the library is configured and built, you can use it in your CMake project with:
target_link_libraries(<my_target> MCFClass::MCFClass)

Using makefiles

  • To create the library, go into lib/ and type
make -f makefile-lib
  • To test the library, go into test and type make.

  • If you want to use the MCFCplex class, which comes commented out by default, uncomment the two lines in lib/makefile:

include $(MCFCxDIR)makefile

Then edit extlib/makefile-libCPLEX to insert the right Cplex path libraries. You can similarly enable (or disable) any solver, both the LGPL ones and those under the academic license, if you have obtained them, by commenting out (or commenting) the corresponding two lines in lib/makefile.

Other stuff

More information about (some of) the implemented algorithms can be found at

A further solver, MCFIntPnt (based on Interior-Point algorithms) has been developed, but it has not yet reached a sufficient maturuty to be distributed; its principles are discussed at

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