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Dropped our current Tarjan-implementation in favour of the path-based algorithm by Gabow (and others) as this seems to perform a lot better (at when comparing our implementations). 

Former-commit-id: 5cfeb85193
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dehnert 11 years ago
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d40573640f
2 changed files with 130 additions and 126 deletions
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  1. 211
      src/storage/StronglyConnectedComponentDecomposition.cpp
  2. 27
      src/storage/StronglyConnectedComponentDecomposition.h

211
src/storage/StronglyConnectedComponentDecomposition.cpp
View File

@ -48,24 +48,85 @@ namespace storm {
template <typename ValueType> template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs) { void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs) {
// Set up the environment of Tarjan's algorithm.
uint_fast64_t numberOfStates = model.getNumberOfStates(); uint_fast64_t numberOfStates = model.getNumberOfStates();
std::vector<uint_fast64_t> tarjanStack;
tarjanStack.reserve(numberOfStates);
storm::storage::BitVector tarjanStackStates(numberOfStates);
std::vector<uint_fast64_t> stateIndices(numberOfStates);
std::vector<uint_fast64_t> lowlinks(numberOfStates);
storm::storage::BitVector visitedStates(numberOfStates);
// Set up the environment of the algorithm.
// Start with the two stacks it maintains.
std::vector<uint_fast64_t> s;
s.reserve(numberOfStates);
std::vector<uint_fast64_t> p;
p.reserve(numberOfStates);
// We also need to store the preorder numbers of states and which states have been assigned to which SCC.
std::vector<uint_fast64_t> preorderNumbers(numberOfStates);
storm::storage::BitVector hasPreorderNumber(numberOfStates);
storm::storage::BitVector stateHasScc(numberOfStates);
std::vector<uint_fast64_t> stateToSccMapping(numberOfStates);
uint_fast64_t sccCount = 0;
// Finally, we need to keep track of the states with a self-loop to identify naive SCCs.
storm::storage::BitVector statesWithSelfLoop(numberOfStates);
// Start the search for SCCs from every state in the block. // Start the search for SCCs from every state in the block.
uint_fast64_t currentIndex = 0; uint_fast64_t currentIndex = 0;
for (auto state : subsystem) { for (auto state : subsystem) {
if (!visitedStates.get(state)) {
performSccDecompositionHelper(model, state, subsystem, currentIndex, stateIndices, lowlinks, tarjanStack, tarjanStackStates, visitedStates, dropNaiveSccs, onlyBottomSccs);
if (!hasPreorderNumber.get(state)) {
performSccDecompositionGCM(model, state, statesWithSelfLoop, subsystem, currentIndex, hasPreorderNumber, preorderNumbers, s, p, stateHasScc, stateToSccMapping, sccCount);
} }
} }
// After we obtained the state-to-SCC mapping, we build the actual blocks.
this->blocks.resize(sccCount);
for (uint_fast64_t state = 0; state < numberOfStates; ++state) {
this->blocks[stateToSccMapping[state]].insert(state);
} }
// If requested, we need to drop some SCCs.
if (onlyBottomSccs || dropNaiveSccs) {
storm::storage::BitVector blocksToDrop(sccCount);
// If requested, we need to delete all naive SCCs.
if (dropNaiveSccs) {
for (uint_fast64_t sccIndex = 0; sccIndex < sccCount; ++sccIndex) {
if (this->blocks[sccIndex].size() == 1) {
uint_fast64_t onlyState = *this->blocks[sccIndex].begin();
if (!statesWithSelfLoop.get(onlyState)) {
blocksToDrop.set(sccIndex);
}
}
}
}
// If requested, we need to drop all non-bottom SCCs.
if (onlyBottomSccs) {
for (uint_fast64_t state = 0; state < numberOfStates; ++state) {
// If the block of the state is already known to be dropped, we don't need to check the transitions.
if (!blocksToDrop.get(stateToSccMapping[state])) {
for (typename storm::storage::SparseMatrix<ValueType>::const_iterator successorIt = model.getRows(state).begin(), successorIte = model.getRows(state).end(); successorIt != successorIte; ++successorIt) {
if (subsystem.get(successorIt->getColumn()) && stateToSccMapping[state] != stateToSccMapping[successorIt->getColumn()]) {
blocksToDrop.set(stateToSccMapping[state]);
break;
}
}
}
}
}
// Create the new set of blocks by moving all the blocks we need to keep into it.
std::vector<Block> newBlocks((~blocksToDrop).getNumberOfSetBits());
uint_fast64_t currentBlock = 0;
for (uint_fast64_t blockIndex = 0; blockIndex < this->blocks.size(); ++blockIndex) {
if (!blocksToDrop.get(blockIndex)) {
newBlocks[currentBlock] = std::move(this->blocks[blockIndex]);
++currentBlock;
}
}
// Now set this new set of blocks as the result of the decomposition.
this->blocks = std::move(newBlocks);
}
}
template <typename ValueType> template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, bool dropNaiveSccs, bool onlyBottomSccs) { void StronglyConnectedComponentDecomposition<ValueType>::performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, bool dropNaiveSccs, bool onlyBottomSccs) {
@ -77,128 +138,68 @@ namespace storm {
} }
template <typename ValueType> template <typename ValueType>
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecompositionHelper(storm::models::AbstractModel<ValueType> const& model, uint_fast64_t startState, storm::storage::BitVector const& subsystem, uint_fast64_t& currentIndex, std::vector<uint_fast64_t>& stateIndices, std::vector<uint_fast64_t>& lowlinks, std::vector<uint_fast64_t>& tarjanStack, storm::storage::BitVector& tarjanStackStates, storm::storage::BitVector& visitedStates, bool dropNaiveSccs, bool onlyBottomSccs) {
// Create the stacks needed for turning the recursive formulation of Tarjan's algorithm into an iterative
// version. In particular, we keep one stack for states and one stack for the iterators. The last one is not
// strictly needed, but reduces iteration work when all successors of a particular state are considered.
std::vector<uint_fast64_t> recursionStateStack;
recursionStateStack.reserve(lowlinks.size());
std::vector<typename storm::storage::SparseMatrix<ValueType>::const_iterator> recursionIteratorStack;
recursionIteratorStack.reserve(lowlinks.size());
std::vector<bool> statesInStack(lowlinks.size());
void StronglyConnectedComponentDecomposition<ValueType>::performSccDecompositionGCM(storm::models::AbstractModel<ValueType> const& model, uint_fast64_t startState, storm::storage::BitVector& statesWithSelfLoop, storm::storage::BitVector const& subsystem, uint_fast64_t& currentIndex, storm::storage::BitVector& hasPreorderNumber, std::vector<uint_fast64_t>& preorderNumbers, std::vector<uint_fast64_t>& s, std::vector<uint_fast64_t>& p, storm::storage::BitVector& stateHasScc, std::vector<uint_fast64_t>& stateToSccMapping, uint_fast64_t& sccCount) {
// Store a bit vector of all states with a self-loop to be able to detect non-trivial SCCs with only one
// state.
storm::storage::BitVector statesWithSelfloop;
if (dropNaiveSccs) {
statesWithSelfloop = storm::storage::BitVector(lowlinks.size());
}
// Initialize the recursion stacks with the given initial state (and its successor iterator).
// Prepare the stack used for turning the recursive procedure into an iterative one.
std::vector<uint_fast64_t> recursionStateStack;
recursionStateStack.reserve(model.getNumberOfStates());
recursionStateStack.push_back(startState); recursionStateStack.push_back(startState);
std::vector<typename storm::storage::SparseMatrix<ValueType>::const_iterator> recursionIteratorStack;
recursionIteratorStack.push_back(model.getRows(startState).begin()); recursionIteratorStack.push_back(model.getRows(startState).begin());
recursionStepForward:
while (!recursionStateStack.empty()) { while (!recursionStateStack.empty()) {
uint_fast64_t currentState = recursionStateStack.back(); uint_fast64_t currentState = recursionStateStack.back();
typename storm::storage::SparseMatrix<ValueType>::const_iterator successorIt = recursionIteratorStack.back();
typename storm::storage::SparseMatrix<ValueType>::const_iterator& successorIt = recursionIteratorStack.back();
// Perform the treatment of newly discovered state as defined by Tarjan's algorithm.
visitedStates.set(currentState, true);
stateIndices[currentState] = currentIndex;
lowlinks[currentState] = currentIndex;
++currentIndex;
tarjanStack.push_back(currentState);
tarjanStackStates.set(currentState, true);
if (!hasPreorderNumber.get(currentState)) {
preorderNumbers[currentState] = currentIndex++;
hasPreorderNumber.set(currentState, true);
// Now, traverse all successors of the current state.
for(; successorIt != model.getRows(currentState).end(); ++successorIt) {
// Record if the current state has a self-loop if we are to drop naive SCCs later.
if (dropNaiveSccs && currentState == successorIt->getColumn()) {
statesWithSelfloop.set(currentState, true);
s.push_back(currentState);
p.push_back(currentState);
} }
// If we have not visited the successor already, we need to perform the procedure recursively on the
// newly found state, but only if it belongs to the subsystem in which we are interested.
bool recursionStepIn = false;
for (; successorIt != model.getRows(currentState).end(); ++successorIt) {
if (subsystem.get(successorIt->getColumn())) { if (subsystem.get(successorIt->getColumn())) {
if (!visitedStates.get(successorIt->getColumn())) {
// Save current iterator position so we can continue where we left off later.
recursionIteratorStack.pop_back();
recursionIteratorStack.push_back(successorIt);
if (currentState == successorIt->getColumn()) {
statesWithSelfLoop.set(currentState);
}
// Put unvisited successor on top of our recursion stack and remember that.
if (!hasPreorderNumber.get(successorIt->getColumn())) {
// In this case, we must recursively visit the successor. We therefore push the state onto the recursion stack an break the for-loop.
recursionStateStack.push_back(successorIt->getColumn()); recursionStateStack.push_back(successorIt->getColumn());
statesInStack[successorIt->getColumn()] = true;
recursionStepIn = true;
// Also, put initial value for iterator on corresponding recursion stack.
recursionIteratorStack.push_back(model.getRows(successorIt->getColumn()).begin()); recursionIteratorStack.push_back(model.getRows(successorIt->getColumn()).begin());
// Perform the actual recursion step in an iterative way.
goto recursionStepForward;
recursionStepBackward:
lowlinks[currentState] = std::min(lowlinks[currentState], lowlinks[successorIt->getColumn()]);
} else if (tarjanStackStates.get(successorIt->getColumn())) {
// Update the lowlink of the current state.
lowlinks[currentState] = std::min(lowlinks[currentState], stateIndices[successorIt->getColumn()]);
}
}
}
// If the current state is the root of a SCC, we need to pop all states of the SCC from the algorithm's
// stack.
if (lowlinks[currentState] == stateIndices[currentState]) {
Block scc;
uint_fast64_t lastState = 0;
do {
// Pop topmost state from the algorithm's stack.
lastState = tarjanStack.back();
tarjanStack.pop_back();
tarjanStackStates.set(lastState, false);
// Add the state to the current SCC.
scc.insert(lastState);
} while (lastState != currentState);
bool isBottomScc = true;
if (onlyBottomSccs) {
for (auto const& state : scc) {
for (auto const& successor : model.getRows(state)) {
if (scc.find(successor.getColumn()) == scc.end()) {
isBottomScc = false;
break; break;
} else {
if (!stateHasScc.get(successorIt->getColumn())) {
while (preorderNumbers[p.back()] > preorderNumbers[successorIt->getColumn()]) {
p.pop_back();
} }
} }
} }
} }
// Now determine whether we want to keep this SCC in the decomposition.
// First, we need to check whether we should drop the SCC because of the requirement to not include
// naive SCCs.
bool keepScc = !dropNaiveSccs || (scc.size() > 1 || statesWithSelfloop.get(*scc.begin()));
// Then, we also need to make sure that it is a bottom SCC if we were required to.
keepScc &= !onlyBottomSccs || isBottomScc;
// Only add the SCC if we determined to keep it, based on the given parameters.
if (keepScc) {
this->blocks.emplace_back(std::move(scc));
} }
if (!recursionStepIn) {
if (currentState == p.back()) {
p.pop_back();
uint_fast64_t poppedState = 0;
do {
poppedState = s.back();
s.pop_back();
stateToSccMapping[poppedState] = sccCount;
stateHasScc.set(poppedState);
} while (poppedState != currentState);
++sccCount;
} }
// If we reach this point, we have completed the recursive descent for the current state. That is, we
// need to pop it from the recursion stacks.
recursionStateStack.pop_back(); recursionStateStack.pop_back();
recursionIteratorStack.pop_back(); recursionIteratorStack.pop_back();
// If there is at least one state under the current one in our recursion stack, we need to restore the
// topmost state as the current state and jump to the part after the original recursive call.
if (recursionStateStack.size() > 0) {
currentState = recursionStateStack.back();
successorIt = recursionIteratorStack.back();
goto recursionStepBackward;
} }
recursionStepIn = false;
} }
} }

27
src/storage/StronglyConnectedComponentDecomposition.h
View File

@ -113,24 +113,27 @@ namespace storm {
void performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs); void performSccDecomposition(storm::models::AbstractModel<ValueType> const& model, storm::storage::BitVector const& subsystem, bool dropNaiveSccs, bool onlyBottomSccs);
/*! /*!
* A helper function that performs the SCC decomposition given all auxiliary data structures. As a
* side-effect this fills the vector of blocks of the decomposition.
* Uses the algorithm by Gabow/Cheriyan/Mehlhorn ("Path-based strongly connected component algorithm") to
* compute a mapping of states to their SCCs. All arguments given by (non-const) reference are modified by
* the function as a side-effect.
* *
* @param model The model to decompose into SCCs. * @param model The model to decompose into SCCs.
* @param startState The starting state for the search of Tarjan's algorithm. * @param startState The starting state for the search of Tarjan's algorithm.
* @param statesWithSelfLoop A bit vector that is to be filled with all states that have a self-loop. This
* is later needed for identification of the naive SCCs.
* @param subsystem The subsystem to search. * @param subsystem The subsystem to search.
* @param currentIndex The next free index that can be assigned to states. * @param currentIndex The next free index that can be assigned to states.
* @param stateIndices A vector storing the index for each state.
* @param lowlinks A vector storing the lowlink for each state.
* @param tarjanStack A vector that is to be used as the stack in Tarjan's algorithm.
* @param tarjanStackStates A bit vector indicating which states are currently in the stack.
* @param visitedStates A bit vector containing all states that have already been visited.
* @param dropNaiveSccs A flag that indicates whether trivial SCCs (i.e. SCCs consisting of just one state
* without a self-loop) are to be kept in the decomposition.
* @param onlyBottomSccs If set to true, only bottom SCCs, i.e. SCCs in which all states have no way of
* leaving the SCC), are kept.
* @param hasPreorderNumber A bit that is used to keep track of the states that already have a preorder number.
* @param preorderNumbers A vector storing the preorder number for each state.
* @param s The stack S used by the algorithm.
* @param p The stack S used by the algorithm.
* @param stateHasScc A bit vector containing all states that have already been assigned to an SCC.
* @param stateToSccMapping A mapping from states to the SCC indices they belong to. As a side effect of this
* function this mapping is filled (for all states reachable from the starting state).
* @param sccCount The number of SCCs that have been computed. As a side effect of this function, this count
* is increased.
*/ */
void performSccDecompositionHelper(storm::models::AbstractModel<ValueType> const& model, uint_fast64_t startState, storm::storage::BitVector const& subsystem, uint_fast64_t& currentIndex, std::vector<uint_fast64_t>& stateIndices, std::vector<uint_fast64_t>& lowlinks, std::vector<uint_fast64_t>& tarjanStack, storm::storage::BitVector& tarjanStackStates, storm::storage::BitVector& visitedStates, bool dropNaiveSccs, bool onlyBottomSccs);
void performSccDecompositionGCM(storm::models::AbstractModel<ValueType> const& model, uint_fast64_t startState, storm::storage::BitVector& statesWithSelfLoop, storm::storage::BitVector const& subsystem, uint_fast64_t& currentIndex, storm::storage::BitVector& hasPreorderNumber, std::vector<uint_fast64_t>& preorderNumbers, std::vector<uint_fast64_t>& s, std::vector<uint_fast64_t>& p, storm::storage::BitVector& stateHasScc, std::vector<uint_fast64_t>& stateToSccMapping, uint_fast64_t& sccCount);
}; };
} }
} }

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