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https://github.com/d-michail/parmcb

Parallel Minimum Cycle Basis
https://github.com/d-michail/parmcb

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Parallel Minimum Cycle Basis

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# 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](https://www.boost.org/) libraries for the underlying

graph implementation. It supports parallel and distributed execution using the

[TBB (Intel Threading Building Blocks)](https://software.intel.com/en-us/tbb) library

and [MPI](https://www.mpi-forum.org/).



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](https://d-michail.github.io/assets/papers/implMCBjournal.pdf),

    [web](https://portal.acm.org/citation.cfm?id=1187436.1216582)



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](http://bit.ly/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](examples/README.md) 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](https://software.intel.com/en-us/articles/installing-intel-free-libs-and-python-apt-repo) 

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](https://www.boost.org/LICENSE_1_0.txt). 

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