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https://github.com/Z3Prover/z3
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network update
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
9467806a5c
commit
bd33e466c2
4 changed files with 578 additions and 137 deletions
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@ -21,6 +21,7 @@ Notes:
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#define _NETWORK_FLOW_DEF_H_
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#include"network_flow.h"
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#include"uint_set.h"
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namespace smt {
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@ -269,7 +270,9 @@ namespace smt {
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}
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template<typename Ext>
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dl_var network_flow<Ext>::find_rev_thread(node n, node ancestor) const {
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dl_var network_flow<Ext>::find_rev_thread(node n) const {
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node ancestor = m_pred[n];
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SASSERT(ancestor != -1);
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while (m_thread[ancestor] != n) {
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ancestor = m_thread[ancestor];
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}
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@ -279,21 +282,19 @@ namespace smt {
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template<typename Ext>
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void network_flow<Ext>::fix_depth(node start, node end) {
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SASSERT(m_pred[start] != -1);
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// Increase depths of all children in T_q by the same amount
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int d = 1 + m_depth[m_pred[start]] - m_depth[start];
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do {
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m_depth[start] += d;
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start = m_thread[start];
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m_depth[start] = m_depth[m_pred[start]]+1;
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while (start != end) {
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start = m_thread[start];
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m_depth[start] = m_depth[m_pred[start]]+1;
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}
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while (start != end);
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}
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/**
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\brief add entering_edge, remove leaving_edge from spanning tree.
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Old tree:
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root
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/ \
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Old tree: New tree:
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root root
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/ \ / \
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x y
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/ \ / \
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u w'
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@ -304,9 +305,6 @@ namespace smt {
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\
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q
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New tree:
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root
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/ \
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x y
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/ \ / \
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u w'
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@ -350,6 +348,7 @@ namespace smt {
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// Initialize m_upwards[q] = q_upwards
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bool prev_upwards = q_upwards;
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#if 0
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for (node n = q, prev = p; n != u; ) {
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SASSERT(m_pred[n] != u || n == v); // the last processed node is v
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node next = m_pred[n];
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@ -360,96 +359,79 @@ namespace smt {
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n = next;
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SASSERT(n != -1);
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}
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#else
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node old_pred = m_pred[q];
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m_pred[q] = p;
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for (node n = q; n != u; ) {
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SASSERT(old_pred != u || n == v); // the last processed node is v
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SASSERT(-1 != m_pred[old_pred]);
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node next_old_pred = m_pred[old_pred];
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swap_order(n, old_pred);
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std::swap(m_upwards[n], prev_upwards);
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prev_upwards = !prev_upwards; // flip previous version of upwards.
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n = old_pred;
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old_pred = next_old_pred;
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}
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// At this point m_pred and m_upwards have been updated.
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TRACE("network_flow", tout << pp_vector("Predecessors", m_pred, true) << pp_vector("Upwards", m_upwards););
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#endif
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//
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node x = m_final[p];
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node y = m_thread[x];
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node z = m_final[q];
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// ----
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// update m_final.
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// Do this before updating data structures
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node gamma_p = m_pred[m_thread[m_final[p]]];
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node gamma_v = m_pred[m_thread[m_final[v]]];
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node theta = m_thread[m_final[v]];
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// Check that f(u) is not in T_v
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bool found_final_u = false;
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for (node n = v; n != theta; n = m_thread[n]) {
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if (n == m_final[u]) {
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found_final_u = true;
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break;
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}
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}
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node phi = find_rev_thread(v, u);
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node delta = found_final_u ? phi : m_final[u];
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TRACE("network_flow", tout << "Graft T_q and T_r'\n";);
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for (node n = p; n != gamma_p && n != -1; n = m_pred[n]) {
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TRACE("network_flow", tout << "1: m_final[" << n << "] |-> " << z << "\n";);
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m_final[n] = z;
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}
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//
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m_thread[x] = q;
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m_thread[z] = y;
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// m_thread and m_final were updated.
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// update the depth.
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fix_depth(q, m_final[q]);
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TRACE("network_flow", tout << "Update T_r'\n";);
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m_thread[phi] = theta;
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for (node n = u; n != gamma_v && n != -1; n = m_pred[n]) {
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TRACE("network_flow", tout << "2: m_final[" << n << "] |-> " << delta << "\n";);
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m_final[n] = delta;
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}
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TRACE("network_flow", tout << pp_vector("Last Successors", m_final, true) << pp_vector("Depths", m_depth););
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if (v != q) {
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TRACE("network_flow", tout << "Reroot T_v at q\n";);
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node alpha1, alpha2;
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node prev = q;
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for (node n = v; n != q && n != -1; n = m_pred[n]) {
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// Find all immediate successors of n
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node t1 = m_thread[n];
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node t2 = m_thread[m_final[t1]];
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node t3 = m_thread[m_final[t2]];
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if (t1 == m_pred[n]) {
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alpha1 = t2;
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alpha2 = t3;
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}
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else if (t2 == m_pred[n]) {
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alpha1 = t1;
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alpha2 = t3;
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}
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else {
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alpha1 = t1;
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alpha2 = t2;
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}
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m_thread[n] = alpha1;
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m_thread[m_final[alpha1]] = alpha2;
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m_thread[m_final[alpha2]] = prev;
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prev = n;
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}
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m_thread[m_final[q]] = prev;
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}
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TRACE("network_flow", {
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tout << pp_vector("Threads", m_thread, true);
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});
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}
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/**
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swap v and q in tree.
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- fixup m_final
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- fixup m_thread
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- fixup m_pred
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Case 1: final(q) == final(v)
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-------
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Old thread: prev -> v -*-> alpha -> q -*-> final(q) -> next
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New thread: prev -> q -*-> final(q) -> v -*-> alpha -> next
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Case 2: final(q) != final(v)
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-------
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Old thread: prev -> v -*-> alpha -> q -*-> final(q) -> beta -*-> final(v) -> next
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New thread: prev -> q -*-> final(q) -> v -*-> alpha -> beta -*-> final(v) -> next
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*/
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template<typename Ext>
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void network_flow<Ext>::swap_order(node q, node v) {
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SASSERT(q != v);
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SASSERT(m_pred[q] == v);
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SASSERT(is_preorder_traversal(v, m_final[v]));
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node prev = find_rev_thread(v);
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node final_q = m_final[q];
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node final_v = m_final[v];
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node next = m_thread[final_v];
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node alpha = find_rev_thread(q);
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if (final_q == final_v) {
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m_thread[final_q] = v;
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m_thread[alpha] = next;
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m_final[q] = alpha;
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m_final[v] = alpha;
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}
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else {
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node beta = m_thread[final_q];
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m_thread[final_q] = v;
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m_thread[alpha] = beta;
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m_final[q] = final_v;
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}
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m_thread[prev] = q;
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m_pred[v] = q;
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SASSERT(is_preorder_traversal(q, m_final[q]));
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}
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template<typename Ext>
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std::string network_flow<Ext>::display_spanning_tree() {
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++m_step;;
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@ -595,7 +577,8 @@ namespace smt {
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Furthermore, the nodes linked in m_thread follows a
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depth-first traversal order.
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m_final[n] is deepest most node in a sub-tree rooted at n.
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m_final[n] is the last node in depth-first traversal order,
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starting from n, that is still a child of n.
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m_upwards direction of edge from i to m_pred[i] m_graph
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@ -670,6 +653,118 @@ namespace smt {
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return true;
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}
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template<typename Ext>
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bool network_flow<Ext>::is_preorder_traversal(node start, node end) {
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// get children of start:
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uint_set children;
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children.insert(start);
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node root = m_pred.size()-1;
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for (int i = 0; i < root; ++i) {
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for (int j = 0; j < root; ++j) {
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if (children.contains(m_pred[j])) {
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children.insert(j);
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}
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}
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}
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// visit children using m_thread
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children.remove(start);
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do {
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start = m_thread[start];
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SASSERT(children.contains(start));
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children.remove(start);
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}
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while (start != end);
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SASSERT(children.empty());
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return true;
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}
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}
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#endif
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#if 0
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// At this point m_pred and m_upwards have been updated.
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TRACE("network_flow", tout << pp_vector("Predecessors", m_pred, true) << pp_vector("Upwards", m_upwards););
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//
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node x = m_final[p];
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node y = m_thread[x];
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node z = m_final[q];
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// ----
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// update m_final.
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// Do this before updating data structures
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node gamma_p = m_pred[m_thread[m_final[p]]];
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node gamma_v = m_pred[m_thread[m_final[v]]];
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node theta = m_thread[m_final[v]];
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// Check that f(u) is not in T_v
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bool found_final_u = false;
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for (node n = v; n != theta; n = m_thread[n]) {
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if (n == m_final[u]) {
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found_final_u = true;
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break;
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}
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}
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node phi = find_rev_thread(v);
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node delta = found_final_u ? phi : m_final[u];
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TRACE("network_flow", tout << "Graft T_q and T_r'\n";);
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for (node n = p; n != gamma_p && n != -1; n = m_pred[n]) {
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TRACE("network_flow", tout << "1: m_final[" << n << "] |-> " << z << "\n";);
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m_final[n] = z;
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}
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//
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m_thread[x] = q;
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m_thread[z] = y;
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TRACE("network_flow", tout << "Update T_r'\n";);
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m_thread[phi] = theta;
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for (node n = u; n != gamma_v && n != -1; n = m_pred[n]) {
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TRACE("network_flow", tout << "2: m_final[" << n << "] |-> " << delta << "\n";);
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m_final[n] = delta;
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}
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TRACE("network_flow", tout << pp_vector("Last Successors", m_final, true) << pp_vector("Depths", m_depth););
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if (v != q) {
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TRACE("network_flow", tout << "Reroot T_v at q\n";);
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node alpha1, alpha2;
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node prev = q;
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for (node n = v; n != q && n != -1; n = m_pred[n]) {
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// Find all immediate successors of n
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node t1 = m_thread[n];
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node t2 = m_thread[m_final[t1]];
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node t3 = m_thread[m_final[t2]];
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if (t1 == m_pred[n]) {
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alpha1 = t2;
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alpha2 = t3;
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}
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else if (t2 == m_pred[n]) {
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alpha1 = t1;
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alpha2 = t3;
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}
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else {
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alpha1 = t1;
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alpha2 = t2;
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}
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m_thread[n] = alpha1;
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m_thread[m_final[alpha1]] = alpha2;
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m_thread[m_final[alpha2]] = prev;
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prev = n;
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}
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m_thread[m_final[q]] = prev;
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}
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#endif
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