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https://github.com/Z3Prover/z3
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expose models, working on network flow
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
686d146cc6
commit
56c4fa8f6d
9 changed files with 497 additions and 441 deletions
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@ -77,9 +77,9 @@ namespace smt {
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protected:
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graph & m_graph;
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svector<edge_state> & m_states;
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vector<numeral> & m_potentials;
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edge_id & m_enter_id;
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vector<numeral> & m_potentials;
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edge_id & m_enter_id;
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bool edge_in_tree(edge_id id) const { return m_states[id] == BASIS; }
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public:
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pivot_rule_impl(graph & g, vector<numeral> & potentials,
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svector<edge_state> & states, edge_id & enter_id)
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@ -88,46 +88,21 @@ namespace smt {
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m_states(states),
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m_enter_id(enter_id) {
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}
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virtual ~pivot_rule_impl() {}
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virtual bool choose_entering_edge() = 0;
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virtual pivot_rule rule() const = 0;
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};
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class first_eligible_pivot : public pivot_rule_impl {
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private:
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edge_id m_next_edge;
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public:
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first_eligible_pivot(graph & g, vector<numeral> & potentials,
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svector<edge_state> & states, edge_id & enter_id) :
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pivot_rule_impl(g, potentials, states, enter_id),
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m_next_edge(0) {
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}
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bool choose_entering_edge() {
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TRACE("network_flow", tout << "choose_entering_edge...\n";);
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int num_edges = m_graph.get_num_edges();
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for (int i = m_next_edge; i < m_next_edge + num_edges; ++i) {
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edge_id id = (i >= num_edges) ? (i - num_edges) : i;
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node src = m_graph.get_source(id);
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node tgt = m_graph.get_target(id);
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if (m_states[id] != BASIS) {
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numeral cost = m_potentials[src] - m_potentials[tgt] - m_graph.get_weight(id);
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if (cost.is_pos()) {
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m_enter_id = id;
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TRACE("network_flow", {
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tout << "Found entering edge " << id << " between node ";
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tout << src << " and node " << tgt << " with reduced cost = " << cost << "...\n";
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});
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m_next_edge = m_enter_id;
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if (m_next_edge >= num_edges) {
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m_next_edge -= num_edges;
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}
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return true;
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}
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}
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}
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TRACE("network_flow", tout << "Found no entering edge...\n";);
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return false;
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};
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virtual bool choose_entering_edge();
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virtual pivot_rule rule() const { return FIRST_ELIGIBLE; }
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};
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class best_eligible_pivot : public pivot_rule_impl {
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@ -136,33 +111,8 @@ namespace smt {
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svector<edge_state> & states, edge_id & enter_id) :
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pivot_rule_impl(g, potentials, states, enter_id) {
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}
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bool choose_entering_edge() {
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TRACE("network_flow", tout << "choose_entering_edge...\n";);
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unsigned num_edges = m_graph.get_num_edges();
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numeral max = numeral::zero();
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for (unsigned i = 0; i < num_edges; ++i) {
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node src = m_graph.get_source(i);
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node tgt = m_graph.get_target(i);
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if (m_states[i] != BASIS) {
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numeral cost = m_potentials[src] - m_potentials[tgt] - m_graph.get_weight(i);
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if (cost > max) {
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max = cost;
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m_enter_id = i;
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}
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}
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}
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if (max.is_pos()) {
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TRACE("network_flow", {
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tout << "Found entering edge " << m_enter_id << " between node ";
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tout << m_graph.get_source(m_enter_id) << " and node " << m_graph.get_target(m_enter_id);
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tout << " with reduced cost = " << max << "...\n";
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});
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return true;
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}
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TRACE("network_flow", tout << "Found no entering edge...\n";);
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return false;
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};
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virtual pivot_rule rule() const { return BEST_ELIGIBLE; }
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virtual bool choose_entering_edge();
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};
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class candidate_list_pivot : public pivot_rule_impl {
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@ -186,94 +136,22 @@ namespace smt {
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m_candidates(m_num_candidates) {
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}
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bool choose_entering_edge() {
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if (m_current_length == 0 || m_minor_step == MINOR_STEP_LIMIT) {
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// Build the candidate list
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unsigned num_edges = m_graph.get_num_edges();
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numeral max = numeral::zero();
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m_current_length = 0;
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for (unsigned i = m_next_edge; i < m_next_edge + num_edges; ++i) {
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edge_id id = (i >= num_edges) ? i - num_edges : i;
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node src = m_graph.get_source(id);
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node tgt = m_graph.get_target(id);
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if (m_states[id] != BASIS) {
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numeral cost = m_potentials[src] - m_potentials[tgt] - m_graph.get_weight(id);
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if (cost.is_pos()) {
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m_candidates[m_current_length] = id;
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++m_current_length;
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if (cost > max) {
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max = cost;
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m_enter_id = id;
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}
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}
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if (m_current_length >= m_num_candidates) break;
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}
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}
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m_next_edge = m_enter_id;
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m_minor_step = 1;
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if (max.is_pos()) {
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TRACE("network_flow", {
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tout << "Found entering edge " << m_enter_id << " between node ";
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tout << m_graph.get_source(m_enter_id) << " and node " << m_graph.get_target(m_enter_id);
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tout << " with reduced cost = " << max << "...\n";
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});
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return true;
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}
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TRACE("network_flow", tout << "Found no entering edge...\n";);
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return false;
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}
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virtual pivot_rule rule() const { return CANDIDATE_LIST; }
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++m_minor_step;
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numeral max = numeral::zero();
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for (unsigned i = 0; i < m_current_length; ++i) {
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edge_id id = m_candidates[i];
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node src = m_graph.get_source(id);
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node tgt = m_graph.get_target(id);
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if (m_states[id] != BASIS) {
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numeral cost = m_potentials[src] - m_potentials[tgt] - m_graph.get_weight(id);
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if (cost > max) {
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max = cost;
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m_enter_id = id;
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}
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// Remove stale candidates
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if (!cost.is_pos()) {
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--m_current_length;
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m_candidates[i] = m_candidates[m_current_length];
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--i;
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}
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}
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}
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if (max.is_pos()) {
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TRACE("network_flow", {
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tout << "Found entering edge " << m_enter_id << " between node ";
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tout << m_graph.get_source(m_enter_id) << " and node " << m_graph.get_target(m_enter_id);
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tout << " with reduced cost = " << max << "...\n";
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});
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return true;
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}
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TRACE("network_flow", tout << "Found no entering edge...\n";);
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return false;
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};
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virtual bool choose_entering_edge();
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};
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graph m_graph;
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spanning_tree_base * m_tree;
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// Denote supply/demand b_i on node i
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vector<fin_numeral> m_balances;
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// Duals of flows which are convenient to compute dual solutions
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vector<numeral> m_potentials;
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// Basic feasible flows
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vector<numeral> m_flows;
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svector<edge_state> m_states;
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unsigned m_step;
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edge_id m_enter_id, m_leave_id;
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optional<numeral> m_delta;
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graph m_graph;
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scoped_ptr<spanning_tree_base> m_tree;
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scoped_ptr<pivot_rule_impl> m_pivot;
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vector<fin_numeral> m_balances; // Denote supply/demand b_i on node i
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vector<numeral> m_potentials; // Duals of flows which are convenient to compute dual solutions
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vector<numeral> m_flows; // Basic feasible flows
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svector<edge_state> m_states;
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unsigned m_step;
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edge_id m_enter_id;
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edge_id m_leave_id;
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optional<numeral> m_delta;
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// Initialize the network with a feasible spanning tree
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void initialize();
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@ -290,6 +168,8 @@ namespace smt {
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void update_spanning_tree();
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numeral get_cost() const;
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bool edge_in_tree(edge_id id) const;
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bool is_infeasible();
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