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base.hpp
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3  * Main authors:
4  * Christian Schulte <schulte@gecode.org>
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7  * Christian Schulte, 2007
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33 
34 namespace Gecode { namespace Int { namespace Circuit {
35 
36  template<class View, class Offset>
39  : NaryPropagator<View,Int::PC_INT_DOM>(home,x),
40  start(0), y(home,x), o(o0) {
41  home.notice(*this,AP_WEAKLY);
42  }
43 
44  template<class View, class Offset>
47  : NaryPropagator<View,Int::PC_INT_DOM>(home,p), start(p.start) {
48  o.update(p.o);
49  y.update(home,p.y);
50  }
51 
53  template<class View>
54  class NodeInfo {
55  public:
56  int min, low, pre;
58  };
59 
61  template<class View>
62  class TellInfo {
63  public:
64  View x; int n;
65  };
66 
67  template<class View, class Offset>
70  int n = x.size();
71 
73  {
74  int v = start;
76  int m = n;
77  while (x[v].assigned()) {
78  m--;
79  v = o(x[v]).val();
80  // Reached start node again, check whether all nodes have been visited
81  if (start == v)
82  return (m == 0) ? home.ES_SUBSUMED(*this) : ES_FAILED;
83  }
84  start = v;
85  }
86 
88  Region r;
89  typedef typename Offset::ViewType OView;
90  NodeInfo<OView>* si = r.alloc<NodeInfo<OView> >(n);
91  unsigned int n_edges = 0;
92  for (int i=0; i<n; i++) {
93  n_edges += x[i].size();
94  si[i].pre=-1;
95  }
96 
97  // Stack to remember which nodes have not been processed completely
99 
100  // Array to remember which mandatory tells need to be done
101  TellInfo<OView>* eq = r.alloc<TellInfo<OView> >(n);
102  int n_eq = 0;
103 
104  // Array to remember which edges need to be pruned
105  TellInfo<OView>* nq = r.alloc<TellInfo<OView> >(n_edges);
106  int n_nq = 0;
107 
108  /*
109  * Check whether there is a single strongly connected component.
110  * This is a downstripped version of Tarjan's algorithm as
111  * the computation of sccs proper is not needed. In addition, it
112  * checks a mandatory condition for a graph to be Hamiltonian
113  * (due to Mats Carlsson).
114  *
115  * To quote Mats: Suppose you do a depth-first search of the graph.
116  * In that search, the root node will have a number of child subtrees
117  * T1, ..., Tn. By construction, if i<j then there is no edge from
118  * Ti to Tj. The necessary condition for Hamiltonianicity is that
119  * there be an edge from Ti+1 to Ti, for 0 < i < n.
120  *
121  * In addition, we do the following: if there is only a single edge
122  * from Ti+1 to Ti, then it must be mandatory and the variable must
123  * be assigned to that value.
124  *
125  * The same holds true for a back edge from T0 to the root node.
126  *
127  * Then, all edges that reach from Ti+k+1 to Ti can be pruned.
128  *
129  */
130 
131  {
132  // Start always at node start
133  int i = start;
134  // Counter for scc
135  int cnt = 0;
136  // Smallest preorder number of last subtree (initially, the root node)
137  int subtree_min = 0;
138  // Largest preorder number of last subtree (initially, the root node)
139  int subtree_max = 0;
140  // Number of back edges into last subtree or root
141  int back = 0;
142  start:
143  si[i].min = si[i].pre = si[i].low = cnt++;
144  si[i].v.init(o(x[i]));
145  do {
146  if (si[si[i].v.val()].pre < 0) {
147  next.push(i);
148  i=si[i].v.val();
149  goto start;
150  } else if ((subtree_min <= si[si[i].v.val()].pre) &&
151  (si[si[i].v.val()].pre <= subtree_max)) {
152  back++;
153  eq[n_eq].x = o(x[i]);
154  eq[n_eq].n = si[i].v.val();
155  } else if (si[si[i].v.val()].pre < subtree_min) {
156  nq[n_nq].x = o(x[i]);
157  nq[n_nq].n = si[i].v.val();
158  n_nq++;
159  }
160  cont:
161  if (si[si[i].v.val()].low < si[i].min)
162  si[i].min = si[si[i].v.val()].low;
163  ++si[i].v;
164  } while (si[i].v());
165  if (si[i].min < si[i].low) {
166  si[i].low = si[i].min;
167  } else if (i != start) {
168  // If it is not the first node visited, there is more than one SCC
169  return ES_FAILED;
170  }
171  if (!next.empty()) {
172  i=next.pop();
173  if (i == start) {
174  // No back edge
175  if (back == 0)
176  return ES_FAILED;
177  // Exactly one back edge, make it mandatory (keep topmost entry)
178  if (back == 1)
179  n_eq++;
180  back = 0;
181  subtree_min = subtree_max+1;
182  subtree_max = cnt-1;
183  }
184  goto cont;
185  }
186 
187  // Whether all nodes have been visited
188  if (cnt != n)
189  return ES_FAILED;
190 
191  /*
192  * Whether there is more than one subtree
193  *
194  * This propagation rule is taken from: Kathryn Glenn Francis,
195  * Peter Stuckey, Explaining Circuit Propagation,
196  * Constraints (2014) 19:1-29.
197  *
198  */
199  if (subtree_min > 1) {
200  for (Int::ViewValues<OView> v(o(x[start])); v(); ++v)
201  if (si[v.val()].pre < subtree_min) {
202  nq[n_nq].x = o(x[v.val()]);
203  nq[n_nq].n = v.val();
204  n_nq++;
205  }
206  }
207 
208  ExecStatus es = ES_FIX;
209  // Assign all mandatory edges
210  while (n_eq-- > 0) {
211  ModEvent me = eq[n_eq].x.eq(home,eq[n_eq].n);
212  if (me_failed(me))
213  return ES_FAILED;
214  if (me_modified(me))
215  es = ES_NOFIX;
216  }
217 
218  // Remove all edges that would require a non-simple cycle
219  while (n_nq-- > 0) {
220  ModEvent me = nq[n_nq].x.nq(home,nq[n_nq].n);
221  if (me_failed(me))
222  return ES_FAILED;
223  if (me_modified(me))
224  es = ES_NOFIX;
225  }
226 
227  // Move start to different node for next run
228  start = o(x[start]).min();
229 
230  return es;
231  }
232  }
233 
234  template<class View, class Offset>
235  ExecStatus
237  // Prunes that partial assigned paths are not completed to cycles
238 
239  int n=x.size();
240 
241  Region r;
242 
243  // The path starting at assigned x[i] ends at x[end[j]] which is
244  // not assigned.
245  int* end = r.alloc<int>(n);
246  for (int i=0; i<n; i++)
247  end[i]=-1;
248 
249  // A stack that records all indices i such that end[i] != -1
251 
252  typedef typename Offset::ViewType OView;
253  for (int i=0; i<y.size(); i++) {
254  assert(!y[i].assigned());
255  // Non-assigned views serve as starting points for assigned paths
257  // Try all connected values
258  do {
259  int j0=v.val();
260  // Starting point for not yet followed assigned path found
261  if (x[j0].assigned() && (end[j0] < 0)) {
262  // Follow assigned path until non-assigned view:
263  // all assigned view on the paths can be skipped, as
264  // if x[i] is assigned to j, then x[j] will only have
265  // x[i] as predecessor due to propagating distinct.
266  int j = j0;
267  do {
268  j=o(x[j]).val();
269  } while (x[j].assigned());
270  // Now there cannot be a cycle from x[j] to x[v.val()]!
271  // However, the tell cannot be done here as j might be
272  // equal to i and might hence kill the iterator v!
273  end[j0]=j; tell.push(j0);
274  }
275  ++v;
276  } while (v());
277  }
278 
279  // Now do the tells based on the end information
280  while (!tell.empty()) {
281  int i = tell.pop();
282  assert(end[i] >= 0);
283  GECODE_ME_CHECK(o(x[end[i]]).nq(home,i));
284  }
285  return ES_NOFIX;
286  }
287 
288  template<class View, class Offset>
289  forceinline size_t
291  home.ignore(*this,AP_WEAKLY);
293  return sizeof(*this);
294  }
295 
296 }}}
297 
298 // STATISTICS: int-prop
299 
int p
Number of positive literals for node type.
Definition: bool-expr.cpp:232
int n
Number of negative literals for node type.
Definition: bool-expr.cpp:234
Node * x
Pointer to corresponding Boolean expression node.
Definition: bool-expr.cpp:249
NNF * r
Right subtree.
Definition: bool-expr.cpp:242
Home class for posting propagators
Definition: core.hpp:856
void notice(Actor &a, ActorProperty p, bool duplicate=false)
Notice actor property.
Definition: core.hpp:3219
Base-class for circuit propagator.
Definition: circuit.hh:55
ExecStatus connected(Space &home)
Check whether the view value graph is strongly connected.
Definition: base.hpp:69
ViewArray< View > y
Array for performing value propagation for distinct.
Definition: circuit.hh:61
Offset o
Offset transformation.
Definition: circuit.hh:63
virtual size_t dispose(Space &home)
Delete propagator and return its size.
Definition: base.hpp:290
ExecStatus path(Space &home)
Ensure path property: prune edges that could give too small cycles.
Definition: base.hpp:236
Base(Space &home, Base &p)
Constructor for cloning p.
Information required for non-recursive checking for a single scc.
Definition: base.hpp:54
Int::ViewValues< View > v
Definition: base.hpp:57
Information for performing a recorded tell.
Definition: base.hpp:62
Offset integer view.
Definition: view.hpp:443
Converter with fixed offset.
Definition: view.hpp:650
void update(const Offset &o)
Update during cloning.
Value iterator for integer views.
Definition: view.hpp:94
n-ary propagator
Definition: pattern.hpp:142
Handle to region.
Definition: region.hpp:55
Computation spaces.
Definition: core.hpp:1742
Stack with fixed number of elements.
void push(const T &x)
Push element x on top of stack.
T pop(void)
Pop topmost element from stack and return it.
bool empty(void) const
Test whether stack is empty.
View arrays.
Definition: array.hpp:253
ExecStatus
Definition: core.hpp:472
@ ES_FIX
Propagation has computed fixpoint.
Definition: core.hpp:477
@ ES_FAILED
Execution has resulted in failure.
Definition: core.hpp:474
@ ES_NOFIX
Propagation has not computed fixpoint.
Definition: core.hpp:475
int ModEvent
Type for modification events.
Definition: core.hpp:62
Post propagator for SetVar SetOpType SetVar y
Definition: set.hh:767
ExecStatus ES_SUBSUMED(Propagator &p)
Definition: core.hpp:3563
void ignore(Actor &a, ActorProperty p, bool duplicate=false)
Ignore actor property.
Definition: core.hpp:4074
#define GECODE_ME_CHECK(me)
Check whether modification event me is failed, and forward failure.
Definition: macros.hpp:52
bool me_failed(ModEvent me)
Check whether modification event me is failed.
Definition: modevent.hpp:54
bool me_modified(ModEvent me)
Check whether modification event me describes variable modification.
Definition: modevent.hpp:59
@ AP_WEAKLY
Definition: core.hpp:568
const FloatNum min
Smallest allowed float value.
Definition: float.hh:846
bool assigned(View x, int v)
Whether x is assigned to value v.
Definition: single.hpp:43
const Gecode::PropCond PC_INT_DOM
Propagate when domain changes.
Definition: var-type.hpp:100
Gecode::IntArgs i({1, 2, 3, 4})
const int v[7]
Definition: distinct.cpp:259
const SetInstr * si[]
Definition: mm-set.cpp:4341
#define forceinline
Definition: config.hpp:192