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/*
* Copyright 2008-2009 NVIDIA Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <cusp/exception.h>
#include <cusp/csr_matrix.h>
#include <cusp/graph/detail/dispatch/maximum_flow.h>
namespace cusp
{
namespace graph
{
namespace detail
{
template<typename MatrixType, typename ArrayType, typename IndexType>
typename MatrixType::value_type
maximum_flow(const MatrixType& G, ArrayType& flow, const IndexType src, const IndexType sink, cusp::csr_format)
{
return cusp::graph::detail::dispatch::maximum_flow(G, flow, src, sink,
typename MatrixType::memory_space());
}
template<typename MatrixType, typename ArrayType1, typename ArrayType2, typename IndexType>
size_t max_flow_to_min_cut(const MatrixType& G, const ArrayType1& flow, const IndexType src, ArrayType2& min_cut_edges, cusp::csr_format)
{
typedef typename MatrixType::value_type ValueType;
typedef typename MatrixType::memory_space MemorySpace;
typedef cusp::csr_matrix_view<
typename MatrixType::row_offsets_array_type,
typename MatrixType::column_indices_array_type,
typename MatrixType::values_array_type> MatrixType_view;
cusp::array1d<IndexType,MemorySpace> row_indices(G.num_entries);
cusp::array1d<ValueType,MemorySpace> residual(G.num_entries);
cusp::array1d<ValueType,MemorySpace> labels(G.num_rows, -1);
// construct row indices
cusp::detail::offsets_to_indices(G.row_offsets, row_indices);
// copy of column indices
cusp::array1d<IndexType,MemorySpace> column_indices(G.column_indices);
// create view using new column indices
MatrixType_view G_view(G.num_rows, G.num_cols, G.num_entries,
G.row_offsets, column_indices, G.values);
// residual is equal to the difference in capacity and flow
cusp::blas::axpby(G.values, flow, residual, 1, -1);
// edges with zero capacity are set to invalid vertex id
thrust::replace_if(G_view.column_indices.begin(), G_view.column_indices.end(),
residual.begin(), thrust::logical_not<IndexType>(), IndexType(-1));
// Construct BFS levels starting from the source
cusp::graph::breadth_first_search<false>(G_view, src, labels);
// partition vertices into sets marked as -1 or 1
thrust::replace_if(labels.begin(), labels.end(), thrust::placeholders::_1 != -1, IndexType(1));
// identify edges spanning both sets
thrust::transform(thrust::make_permutation_iterator(labels.begin(), row_indices.begin()),
thrust::make_permutation_iterator(labels.begin(), row_indices.end()),
thrust::make_permutation_iterator(labels.begin(), G.column_indices.begin()),
min_cut_edges.begin(), thrust::not_equal_to<IndexType>());
return thrust::reduce(min_cut_edges.begin(), min_cut_edges.end());
}
//////////////////
// General Path //
//////////////////
template<typename MatrixType, typename ArrayType, typename IndexType, typename Format>
typename MatrixType::value_type
size_tmaximum_flow(const MatrixType& G, ArrayType& flow, const IndexType src, const IndexType sink, Format)
{
typedef typename MatrixType::value_type ValueType;
typedef typename MatrixType::memory_space MemorySpace;
// convert matrix to CSR format and compute on the host
cusp::csr_matrix<IndexType,ValueType,MemorySpace> G_csr(G);
return cusp::graph::maximum_flow(G_csr, flow, src, sink);
}
template<typename MatrixType, typename ArrayType1, typename ArrayType2, typename IndexType, typename Format>
size_t max_flow_to_min_cut(const MatrixType& G, const ArrayType1& flow, const IndexType src, ArrayType2& min_cut_edges, Format)
{
typedef typename MatrixType::value_type ValueType;
typedef typename MatrixType::memory_space MemorySpace;
// convert matrix to CSR format and compute on the host
cusp::csr_matrix<IndexType,ValueType,MemorySpace> G_csr(G);
return cusp::graph::max_flow_to_min_cut(G_csr, flow, src, min_cut_edges);
}
} // end namespace detail
/////////////////
// Entry Point //
/////////////////
template<typename MatrixType, typename ArrayType, typename IndexType>
typename MatrixType::value_type
maximum_flow(const MatrixType& G, ArrayType& flow, const IndexType src, const IndexType sink)
{
CUSP_PROFILE_SCOPED();
if(G.num_rows != G.num_cols)
throw cusp::invalid_input_exception("matrix must be square");
return cusp::graph::detail::maximum_flow(G, flow, src, sink,
typename MatrixType::format());
}
template<typename MatrixType, typename IndexType>
typename MatrixType::value_type
maximum_flow(const MatrixType& G, const IndexType src, const IndexType sink)
{
typedef typename MatrixType::value_type ValueType;
typedef typename MatrixType::memory_space MemorySpace;
cusp::array1d<ValueType,MemorySpace> flow(G.num_entries);
return cusp::graph::detail::maximum_flow(G, flow, src, sink,
typename MatrixType::format());
}
template<typename MatrixType, typename ArrayType1, typename ArrayType2, typename IndexType>
size_t max_flow_to_min_cut(const MatrixType& G, const ArrayType1& flow, const IndexType src, ArrayType2& min_cut_edges)
{
CUSP_PROFILE_SCOPED();
if(G.num_rows != G.num_cols)
throw cusp::invalid_input_exception("matrix must be square");
return cusp::graph::detail::max_flow_to_min_cut(G, flow, src, min_cut_edges,
typename MatrixType::format());
}
} // end namespace graph
} // end namespace cusp
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