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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 <cmath>
#include <vector>
#include <iostream>
#include <queue>
#include <thrust/fill.h>
#include <thrust/replace.h>
#include <cusp/exception.h>
namespace cusp
{
namespace graph
{
namespace detail
{
namespace host
{
using namespace thrust::placeholders;
template<typename VertexId, typename Value>
class PushRelabel {
int N;
const cusp::csr_matrix<VertexId,Value,cusp::host_memory>& G;
cusp::array1d<Value,cusp::host_memory>& flow;
cusp::array1d<Value, cusp::host_memory> excess;
cusp::array1d<int, cusp::host_memory> dist, active, count;
std::queue<int> Q;
void Enqueue(int v) {
if (!active[v] && excess[v] > 0) {
active[v] = true;
Q.push(v);
}
}
void Push(int e) { // e is the edge offset
// TODO : This impacts performance significantly, one binary search per Push operation
VertexId from = thrust::upper_bound(G.row_offsets.begin(), G.row_offsets.end(), e) - G.row_offsets.begin() - 1;
VertexId to = G.column_indices[e];
int amt = int(min(excess[from], Value(G.values[e] - flow[e])));
if (dist[from] <= dist[to] || amt == 0) return;
flow[e] += amt;
// TODO : Need to map edges to their symmetric partner, iterating is constant overhead
for(int i = G.row_offsets[to]; i < G.row_offsets[to + 1]; i++)
if( G.column_indices[i] == from ){ flow[i] -= amt; break; }
excess[to] += amt;
excess[from] -= amt;
Enqueue(to);
}
void Gap(int k) {
for (int v = 0; v < N; v++) {
if (dist[v] < k) continue;
count[dist[v]]--;
dist[v] = max(dist[v], N+1);
count[dist[v]]++;
Enqueue(v);
}
}
void Relabel(int v) {
count[dist[v]]--;
dist[v] = 2*N;
for (int i = G.row_offsets[v]; i < G.row_offsets[v + 1]; i++)
if ((G.values[i] - flow[i]) > 0)
dist[v] = std::min(dist[v], dist[G.column_indices[i]] + 1);
count[dist[v]]++;
Enqueue(v);
}
void Discharge(int v) {
for (int i = G.row_offsets[v]; excess[v] > 0 && i < G.row_offsets[v + 1]; i++) Push(i);
if (excess[v] > 0) {
if (count[dist[v]] == 1)
Gap(dist[v]);
else
Relabel(v);
}
}
public:
template<typename MatrixType, typename ArrayType>
PushRelabel(const MatrixType& graph, ArrayType& flow) : N(graph.num_rows), G(graph), flow(flow), excess(N,Value(0)), dist(N,0), active(N,0), count(2*N,0)
{
// initialize flow
thrust::fill(flow.begin(), flow.end(), Value(0));
}
Value GetMaxFlow(VertexId s, VertexId t) {
count[0] = N-1;
count[N] = 1;
dist[s] = N;
active[s] = active[t] = true;
for (int i = G.row_offsets[s]; i < G.row_offsets[s + 1]; i++) {
excess[s] += G.values[i]; // capacity
Push(i); // Push to location of the edge in reference
}
while (!Q.empty()) {
int v = Q.front();
Q.pop();
active[v] = false;
Discharge(v);
}
Value totflow = 0;
for (int i = G.row_offsets[s]; i < G.row_offsets[s + 1]; i++) totflow += flow[i];
return totflow;
}
};
template<typename MatrixType, typename ArrayType, typename IndexType>
typename MatrixType::value_type
maximum_flow(const MatrixType& G, ArrayType& flow, const IndexType src, const IndexType sink)
{
typedef typename MatrixType::value_type ValueType;
typedef typename MatrixType::memory_space MemorySpace;
PushRelabel<IndexType,ValueType> flow_solver(G, flow);
ValueType max_flow = flow_solver.GetMaxFlow(src, sink);
thrust::replace_if(flow.begin(), flow.end(), _1 < ValueType(0), ValueType(0));
return max_flow;
}
} // end namespace host
} // end namespace detail
} // end namespace graph
} // end namespace cusp
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