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//===----------- ReductionRules.h - Reduction Rules -------------*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Reduction Rules.
//
//===----------------------------------------------------------------------===//
#ifndef LLVM_REDUCTIONRULES_H
#define LLVM_REDUCTIONRULES_H
#include "Graph.h"
#include "Math.h"
#include "Solution.h"
namespace PBQP {
/// \brief Reduce a node of degree one.
///
/// Propagate costs from the given node, which must be of degree one, to its
/// neighbor. Notify the problem domain.
template <typename GraphT>
void applyR1(GraphT &G, typename GraphT::NodeId NId) {
typedef typename GraphT::NodeId NodeId;
typedef typename GraphT::EdgeId EdgeId;
typedef typename GraphT::Vector Vector;
typedef typename GraphT::Matrix Matrix;
typedef typename GraphT::RawVector RawVector;
assert(G.getNodeDegree(NId) == 1 &&
"R1 applied to node with degree != 1.");
EdgeId EId = *G.adjEdgeIds(NId).begin();
NodeId MId = G.getEdgeOtherNodeId(EId, NId);
const Matrix &ECosts = G.getEdgeCosts(EId);
const Vector &XCosts = G.getNodeCosts(NId);
RawVector YCosts = G.getNodeCosts(MId);
// Duplicate a little to avoid transposing matrices.
if (NId == G.getEdgeNode1Id(EId)) {
for (unsigned j = 0; j < YCosts.getLength(); ++j) {
PBQPNum Min = ECosts[0][j] + XCosts[0];
for (unsigned i = 1; i < XCosts.getLength(); ++i) {
PBQPNum C = ECosts[i][j] + XCosts[i];
if (C < Min)
Min = C;
}
YCosts[j] += Min;
}
} else {
for (unsigned i = 0; i < YCosts.getLength(); ++i) {
PBQPNum Min = ECosts[i][0] + XCosts[0];
for (unsigned j = 1; j < XCosts.getLength(); ++j) {
PBQPNum C = ECosts[i][j] + XCosts[j];
if (C < Min)
Min = C;
}
YCosts[i] += Min;
}
}
G.setNodeCosts(MId, YCosts);
G.disconnectEdge(EId, MId);
}
template <typename GraphT>
void applyR2(GraphT &G, typename GraphT::NodeId NId) {
typedef typename GraphT::NodeId NodeId;
typedef typename GraphT::EdgeId EdgeId;
typedef typename GraphT::Vector Vector;
typedef typename GraphT::Matrix Matrix;
typedef typename GraphT::RawMatrix RawMatrix;
assert(G.getNodeDegree(NId) == 2 &&
"R2 applied to node with degree != 2.");
const Vector &XCosts = G.getNodeCosts(NId);
typename GraphT::AdjEdgeItr AEItr = G.adjEdgeIds(NId).begin();
EdgeId YXEId = *AEItr,
ZXEId = *(++AEItr);
NodeId YNId = G.getEdgeOtherNodeId(YXEId, NId),
ZNId = G.getEdgeOtherNodeId(ZXEId, NId);
bool FlipEdge1 = (G.getEdgeNode1Id(YXEId) == NId),
FlipEdge2 = (G.getEdgeNode1Id(ZXEId) == NId);
const Matrix *YXECosts = FlipEdge1 ?
new Matrix(G.getEdgeCosts(YXEId).transpose()) :
&G.getEdgeCosts(YXEId);
const Matrix *ZXECosts = FlipEdge2 ?
new Matrix(G.getEdgeCosts(ZXEId).transpose()) :
&G.getEdgeCosts(ZXEId);
unsigned XLen = XCosts.getLength(),
YLen = YXECosts->getRows(),
ZLen = ZXECosts->getRows();
RawMatrix Delta(YLen, ZLen);
for (unsigned i = 0; i < YLen; ++i) {
for (unsigned j = 0; j < ZLen; ++j) {
PBQPNum Min = (*YXECosts)[i][0] + (*ZXECosts)[j][0] + XCosts[0];
for (unsigned k = 1; k < XLen; ++k) {
PBQPNum C = (*YXECosts)[i][k] + (*ZXECosts)[j][k] + XCosts[k];
if (C < Min) {
Min = C;
}
}
Delta[i][j] = Min;
}
}
if (FlipEdge1)
delete YXECosts;
if (FlipEdge2)
delete ZXECosts;
EdgeId YZEId = G.findEdge(YNId, ZNId);
if (YZEId == G.invalidEdgeId()) {
YZEId = G.addEdge(YNId, ZNId, Delta);
} else {
const Matrix &YZECosts = G.getEdgeCosts(YZEId);
if (YNId == G.getEdgeNode1Id(YZEId)) {
G.setEdgeCosts(YZEId, Delta + YZECosts);
} else {
G.setEdgeCosts(YZEId, Delta.transpose() + YZECosts);
}
}
G.disconnectEdge(YXEId, YNId);
G.disconnectEdge(ZXEId, ZNId);
// TODO: Try to normalize newly added/modified edge.
}
// \brief Find a solution to a fully reduced graph by backpropagation.
//
// Given a graph and a reduction order, pop each node from the reduction
// order and greedily compute a minimum solution based on the node costs, and
// the dependent costs due to previously solved nodes.
//
// Note - This does not return the graph to its original (pre-reduction)
// state: the existing solvers destructively alter the node and edge
// costs. Given that, the backpropagate function doesn't attempt to
// replace the edges either, but leaves the graph in its reduced
// state.
template <typename GraphT, typename StackT>
Solution backpropagate(GraphT& G, StackT stack) {
typedef GraphBase::NodeId NodeId;
typedef typename GraphT::Matrix Matrix;
typedef typename GraphT::RawVector RawVector;
Solution s;
while (!stack.empty()) {
NodeId NId = stack.back();
stack.pop_back();
RawVector v = G.getNodeCosts(NId);
for (auto EId : G.adjEdgeIds(NId)) {
const Matrix& edgeCosts = G.getEdgeCosts(EId);
if (NId == G.getEdgeNode1Id(EId)) {
NodeId mId = G.getEdgeNode2Id(EId);
v += edgeCosts.getColAsVector(s.getSelection(mId));
} else {
NodeId mId = G.getEdgeNode1Id(EId);
v += edgeCosts.getRowAsVector(s.getSelection(mId));
}
}
s.setSelection(NId, v.minIndex());
}
return s;
}
}
#endif // LLVM_REDUCTIONRULES_H
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