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******************************************************************
*                                                                *
*    RegionPushRelabel - Version 1.09                            *
*       A parallel out-of-core cache-oblivious FIFO push-relabel *
*       algorithm for graphs with a regular structure.           *
*    http://vision.csd.uwo.ca/code/                              *
*                                                                *
*    Sameh Khamis (sameh@umiacs.umd.edu)                         *
*    2010-2011                                                   *
*                                                                *
******************************************************************

1. Introduction.

This algorithm was developed by Sameh Khamis at the University of Western Ontario
and extends the work presented in

    "A Scalable Graph-Cut Algorithm for N-D Grids."
    Andrew Delong and Yuri Boykov.
    In IEEE Computer Vision and Pattern Recognition (CVPR), 
    June 2008

If you use this software for non-commercial research purposes, you should cite
the aforementioned paper in any resulting publication.

This software was tested on Windows using Visual Studio 2008 and on GNU/Linux using GCC 4.4.1.
The Boost C++ libraries are required and versions 1.39 and 1.43 were tested.
To build Boost on Windows, please refer to:
http://www.boost.org/doc/libs/1_38_0/more/getting_started/windows.html


****************************************************************************************************

2. License & disclaimer.

    Copyright 2010-2011 Sameh Khamis (sameh@umiacs.umd.edu).
    This software can be used under GPLv2 for non-commercial research purposes only.

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
    A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
    OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


****************************************************************************************************

3. Revision history

v1.09 - bug fix (thanks to Ankit Chaudhary)
v1.08 - another gcc incompatibility fixed (thanks to Tahir Majeed)
v1.07 - better parameter default values
v1.06 - graph size can be runtime-specified and is no longer required
        to be a multiple of the block size, example problem fixed
v1.05 - gcc incompatibility fix (thanks to Matt Gibson)
v1.04 - segmentation bug fix (thanks to Jan Ruegg)
v1.03 - another minor bug fix
v1.02 - minor bug fix (thanks to Alexander Shekhovtsov)
v1.01 - compiles with gcc
v1.00 - initial release


****************************************************************************************************

4. Example usage.

This section shows how to use the library to compute
a minimum cut on the following graph:

                   SOURCE                               Graph
                   /                                 Regularity
                  \/ 100
                (0) --5-> (1) --1-> (2) --5-> (3)            /
                / 5       / 5      / 5      5 /        -- (Node) --
               \/        \/       \/         \/            /
             (4) --5-> (5) --2-> (6) --5-> (7)
             / 5       / 5       / 5      5 /
            \/        \/        \/         \/
          (8)       (9)      (10) --5-> (11)
          / 5       / 5       / 5      5 /
         \/        \/        \/         \/
       (12) -5-> (13) -3-> (14) -5-> (15)
                                     /
                                    \/ 100
                                  SINK

Notes: the library is designed to handle graphs with regular structure.
The four edges shown repeat for every node, including boundary nodes
(e.g, node 3 is connected to node 6, etc.). The repeating structure is called
a cell. Each node in the cell is described by a cell index. The above cell
has a single node. The source and the sink are connected to all the graph nodes.
Building the graph, any omitted edges are assumed to have zero capacities.

For more details refer to:
http://vision.csd.uwo.ca/viki/Graph_regularity_DIMACS_conventions

The code to find the maximum flow and the node labels of this graph is
provided in the bundled Example.cpp. You should also use this file to ensure
your dependencies are set up properly.

/////////////////////////////////////////////////////////////////////////////////

The bundled DimacsReader template class can also be used to compute a maximum flow
on graphs in the DIMACS format. For example, to read in the graph above
from a DIMACS file, you need to first include "DimacsReader.h".

#include "DimacsReader.h"

Then you need to define your graph class as shown above, and create a DimacsReader
template class with your graph class as the template parameter.

typedef DimacsReader<RegularGraph> Reader;

And finally you can use your reader to read in the graph from a DIMACS file.
The graph dimensions must be passed in the second constructor argument.

long dimensions[] = {256, 256, 256};
Reader reader("graph.max", dimensions);
reader.parse();
RegularGraph* g = reader.get_solver();
g->compute_maxflow();

Note: you should NOT delete the RegularGraph object returned by get_solver.


****************************************************************************************************

5. Additional notes.

= The Layout class requires 2 parameters: the offset array and the block dimensions.

*** The offset array is a Boost MPL vector. For arrays with 50 arcs or less, you can use the type Array as shown
in the example above. If you need more than 50 arcs, you should replace Array with mpl::vectorN, with N being
the number of arcs, and include the appropriate header file. For example, vector30.hpp contains mpl::vector24.

*** The block dimensions can be specified using the class BlockDimensions. One limitation exists on the block
dimensions; each block dimension must be greater than the largest absolute edge offset in that dimension. This
implies that the majority of nodes in a block will only be connected to nodes in the same block, improving the
locality and allowing per-block processing.


= The RegionPushRelabel class requires 2 positional parameters, capacity type and flow type, followed by
7 keyword (unordered) parameters, 1 of which is required (the Layout class), and the rest are optional.

The optional parameters are:

*** ThreadCount is the number of worker threads to run. With smaller block sizes, more threads will
likely increase the performance.

*** MaxBlocksPerRegion is the maximum number of blocks each thread will work on. A good rule of thumb
is to set it to the size of the node neighborhood. Having a number of blocks per thread smaller than
the size of the node neighborhood can cause a thread to fail to discharge the flow of a block completely
in one go, increasing the time needed to finish. Having a number of blocks per thread significantly larger
than the size of the node neighborhood can cause threads to starve waiting for work, which affects the
performance gain of having more than one thread.

*** DischargesPerBlock is the number of discharge operations performed on each block, before checking
for gaps to relabel. A good rule of thumb is to set it to a small multiple of the number of nodes in
a block. If this number is set too low, a thread will check for gaps too often and take more time
to finish. If this number is set too high, performance gains that can be achieved by gap relabeling
nodes will be affected.

*** BucketDensity is the number of labels to use in every label bucket for gap relabeling. This is
for systems with limited memory, otherwise it should be 1. For systems with limited memory, setting
this number to an integer greater than 1 will cause gap relabeling to occur less often since nodes
of different labels will be aggregated into a single bucket.

*** BlocksPerMemoryPage is the number of blocks in each memory block. This is also for systems with
limited memory, and can be tweaked to reduce the memory footprint of the algorithm. If the entire
graph can fit in memory, the parameter would not affect the performance, otherwise, trial and error
is best to find a good fit.

*** GlobalUpdateFrequency is the frequency of the global update event. Trial and error might be
necessary to find a good parameter value for a graph.


****************************************************************************************************

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A parallel out-of-core push-relabel algorithm for massive graphs with a regular structure

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