Parallel Minimum Cycle Basis Library

This project implements algorithms to compute exact and approximate Minimum Cycle Bases of weighted graphs. The library is written in C++-14 using the Boost Graph libraries for the underlying graph implementation. It supports parallel and distributed execution using the TBB (Intel Threading Building Blocks) library and MPI.

An older package containing several sequential minimum cycle basis algorithms, using the LEDA library, can be found at https://github.com/d-michail/mcb.

Cite

If you use this package please cite the following paper:

• K. Mehlhorn and D. Michail. Implementing Minimum Cycle Basis Algorithms. ACM Journal of Experimental Algorithmics, 11(2):1-14, 2006. pdf, web

Citing software is just as important as citing any other important sources in your research. If you’re not sure whether or not to cite something, Shouldacite can help you decide if you should.

Algorithms

Undirected Graphs

The following functions are available which implement different algorithmic variants. All of them use a technique called support vector approach in order to establish linear independence. Their main differences are how they compute the actual cycles.

• signed graph
  • mcb_sva_signed
  • mcb_sva_signed_tbb
  • mcb_sva_signed_tbb_mpi
• cycles collection from a feedback vertex set
  • mcb_sva_fvs_trees
  • mcb_sva_fvs_trees_tbb
  • mcb_sva_fvs_trees_mpi
  • mcb_sva_fvs_trees_tbb_mpi
• isometric cycles collection
  • mcb_sva_iso_trees
  • mcb_sva_iso_trees_tbb
  • mcb_sva_iso_trees_mpi
  • mcb_sva_iso_trees_tbb_mpi

All these different implementations support weighted undirected graphs which (a) do not contain self-loops, (b) do not contain multiple edges, and (c) all edge weights are positive. If your graph has self-loops, multiple edges or zero weight edges, you need to handle those in a preprocessing step.

Undirected Graphs (approximation algorithms)

A (2k-1)-approximate algorithm for any integer k >= 1.

• signed graph
  • approx_mcb_sva_signed
• cycles collection from a feedback vertex set
  • approx_mcb_sva_fvs_trees
• isometric cycles collection
  • approx_mcb_sva_iso_trees

The signed graph variation approx_mcb_sva_signed has time complexity equal to
O( m n^{1+1/k} + min(m^3 + m n^2 \log n, n^{3+3/k}) ). The approximation algorithms support weighted undirected graphs with positive edge weights. Multiple edges and self-loops are handled correctly by the algorithm. If you have zero length edges you need to handle them in a preprocessing step.

Two demos programs are included which read a graph in DIMACS format and compute a minimum cycle basis.

Examples

See examples/README for a few basic examples to get you started.

Develop

In order to build the library you need to have CMake installed. A C++-14 compiler is required, such as GCC or Clang.

Using Eclipse

Assume the source file is downloaded in a folder called parmcb. Create a folder called parmcb-build parallel to the parmcb folder. This works best when using Eclipse.

Switch to your new folder parmcb-build and issue

cmake ../parmcb/ -G"Eclipse CDT4 - Unix Makefiles" -DCMAKE_BUILD_TYPE=Release

in order to build without debugging symbols. Use Debug if debugging symbols are required. Open up Eclipse and import an existing project into the workspace.

Using Clang

Use

CC=/usr/bin/clang CXX=/usr/bin/clang++ cmake ../parmcb/ -G"Eclipse CDT4 - Unix Makefiles" -DCMAKE_BUILD_TYPE=Release

Custom TBB location

See the following guide on how to install TBB in Ubuntu based systems.

If cmake fails to locate TBB, try something like

TBBROOT=/apps/compilers/intel/19.0.1/tbb cmake ../parmcb/

or

TBBROOT=/opt/intel/oneapi/tbb/2021.9.0 cmake ../parmcb/ -G"Eclipse CDT4 - Unix Makefiles" -DCMAKE_BUILD_TYPE=Release

Logging

The library has some log statements at various locations that can be helpful. To compile with these statements use the parameter PARMCB_LOGGING as shown in the following:

cmake ../parmcb/ -G"Eclipse CDT4 - Unix Makefiles" -DCMAKE_BUILD_TYPE=Debug -DPARMCB_LOGGING=ON

Linker errors

If you are experiencing any linker errors with the boost libraries, then you boost libraries might have been compiled with an older ABI. In that case a possible workaround is to use

add_definitions(-D_GLIBCXX_USE_CXX11_ABI=0)

in the CMakeLists.txt file.

Happy coding!

License

The library may be used under the terms of the Boost Software License, Version 1.0. Please note that the library is distributed WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Please refer to the license for details.

SPDX-License-Identifier: BSL-1.0

Author

(C) Copyright 2019-2023, by Dimitrios Michail