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Gecode::Int::Sorted

Gecode::Int::Sorted Namespace Reference

Sorted propagators More...

Classes

class  Rank
 Storage class for mininmum and maximum of a variable. More...
class  SccComponent
 Representation of a strongly connected component. More...
class  OfflineMinItem
 Item used to construct the OfflineMin sequence. More...
class  OfflineMin
 Offline-Min datastructure Used to compute the perfect matching between the unsorted views x and the sorted views y. More...
class  TupleMaxInc
 Index comparison for ViewArray<Tuple>. More...
class  TupleMaxIncExt
 Extended Index comparison for ViewArray<Tuple>. More...
class  TupleMinInc
 View comparison on ViewTuples. More...
class  ViewPair
 Pair of views. More...
class  TupleMinIncExt
 Extended view comparison on pairs of views. More...
class  Sorted
 Bounds consistent sortedness propagator. More...

Functions

template<class View >
bool glover (ViewArray< View > &x, ViewArray< View > &y, int tau[], int phi[], OfflineMinItem sequence[], int vertices[])
 Glover's maximum matching in a bipartite graph.
template<class View >
bool revglover (ViewArray< View > &x, ViewArray< View > &y, int tau[], int phiprime[], OfflineMinItem sequence[], int vertices[])
 Symmetric glover function for the upper domain bounds.
template<class View >
void computesccs (ViewArray< View > &x, ViewArray< View > &y, int phi[], SccComponent sinfo[], int scclist[])
 Compute the sccs of the oriented intersection-graph.
template<class View , bool Perm>
bool narrow_domx (Space &home, ViewArray< View > &x, ViewArray< View > &y, ViewArray< View > &z, int tau[], int[], int scclist[], SccComponent sinfo[], bool &nofix)
 Narrowing the domains of the x variables.
template<class View >
bool narrow_domy (Space &home, ViewArray< View > &x, ViewArray< View > &y, int phi[], int phiprime[], bool &nofix)
 Narrowing the domains of the y views.
template<class View , bool Perm>
void sort_sigma (ViewArray< View > &x, ViewArray< View > &z)
 Build $\sigma$.
template<class View , bool Perm>
void sort_tau (ViewArray< View > &x, ViewArray< View > &z, int tau[])
 Build $\tau$.
template<class View >
bool normalize (Space &home, ViewArray< View > &y, ViewArray< View > &x, bool &nofix)
 Performing normalization on the views in y.
template<class View >
bool perm_bc (Space &home, int tau[], SccComponent sinfo[], int scclist[], ViewArray< View > &x, ViewArray< View > &z, bool &crossingedge, bool &nofix)
 Bounds consistency on the permutation views.
template<class View , bool Perm>
ExecStatus bounds_propagation (Space &home, Propagator &p, ViewArray< View > &x, ViewArray< View > &y, ViewArray< View > &z, bool &repairpass, bool &nofix, bool &match_fixed)
 Perform bounds consistent sortedness propagation.
template<class View , bool Perm>
bool check_subsumption (ViewArray< View > &x, ViewArray< View > &y, ViewArray< View > &z, bool &subsumed, int &dropfst)
 Subsumption test.
template<class View , bool Perm>
bool array_assigned (Space &home, ViewArray< View > &x, ViewArray< View > &y, ViewArray< View > &z, bool &subsumed, bool &match_fixed, bool &, bool &noperm_bc)
 Check for assignment of a variable array.
template<class View >
bool channel (Space &home, ViewArray< View > &x, ViewArray< View > &y, ViewArray< View > &z, bool &nofix)
 Channel between x, y and z.

Detailed Description

Sorted propagators

Function Documentation

template<class View >
bool Gecode::Int::Sorted::glover ( ViewArray< View > &  x,
ViewArray< View > &  y,
int  tau[],
int  phi[],
OfflineMinItem  sequence[],
int  vertices[] 
) [inline]

Glover's maximum matching in a bipartite graph.

Compute a matching in the bipartite convex intersection graph with one partition containing the x views and the other containing the y views. The algorithm works with an implicit array structure of the intersection graph.

Union-Find Implementation of F.Glover's matching algorithm.

The idea is to mimick a priority queue storing x-indices $[i_0,\dots, i_{n-1}]$, s.t. the upper domain bounds are sorted $D_{i_0} \leq\dots\leq D_{i_{n-1}}$ where $ D_{i_0}$ is the top element

Definition at line 55 of file matching.hpp.

template<class View >
bool Gecode::Int::Sorted::revglover ( ViewArray< View > &  x,
ViewArray< View > &  y,
int  tau[],
int  phiprime[],
OfflineMinItem  sequence[],
int  vertices[] 
) [inline]

Symmetric glover function for the upper domain bounds.

Definition at line 114 of file matching.hpp.

template<class View >
void Gecode::Int::Sorted::computesccs ( ViewArray< View > &  x,
ViewArray< View > &  y,
int  phi[],
SccComponent  sinfo[],
int  scclist[] 
) [inline]

Compute the sccs of the oriented intersection-graph.

An y-node $y_j$ and its corresponding matching mate $x_{\phi(j)}$ form the smallest possible scc, since both edges $e_1(y_j, x_{\phi(j)})$ and $e_2(x_{\phi(j)},y_j)$ are both contained in the oriented intersection graph.

Hence a scc containg more than two nodes is represented as an array of SccComponent entries, $[ y_{j_0},x_{\phi(j_0)},\dots,y_{j_k},x_{\phi(j_k)}]$.

Parameters scclist ~ resulting sccs

Definition at line 54 of file narrowing.hpp.

template<class View , bool Perm>
bool Gecode::Int::Sorted::narrow_domx ( Space &  home,
ViewArray< View > &  x,
ViewArray< View > &  y,
ViewArray< View > &  z,
int  tau[],
int  [],
int  scclist[],
SccComponent  sinfo[],
bool &  nofix 
) [inline]

Narrowing the domains of the x variables.

Due to the correspondance between perfect matchings in the "reduced" intersection graph of x and y views and feasible assignments for the sorted constraint the new domain bounds for views in x are computed as

  • lower bounds: $ S_i \geq E_l $ where $y_l$ is the leftmost neighbour of $x_i$
  • upper bounds: $ S_i \leq E_h $ where $y_h$ is the rightmost neighbour of $x_i$

Definition at line 130 of file narrowing.hpp.

template<class View >
bool Gecode::Int::Sorted::narrow_domy ( Space &  home,
ViewArray< View > &  x,
ViewArray< View > &  y,
int  phi[],
int  phiprime[],
bool &  nofix 
) [inline]

Narrowing the domains of the y views.

analogously to the x views we take

  • for the upper bounds the matching $\phi$ computed in glover and compute the new upper bound by $T_j=min(E_j, D_{\phi(j)})$
  • for the lower bounds the matching $\phi'$ computed in revglover and update the new lower bound by $T_j=max(E_j, D_{\phi'(j)})$

Definition at line 222 of file narrowing.hpp.

template<class View , bool Perm>
void Gecode::Int::Sorted::sort_sigma ( ViewArray< View > &  x,
ViewArray< View > &  z 
) [inline]

Build $\sigma$.

Creates a sorting permutation $\sigma$ by sorting the views in x according to their lower bounds

Definition at line 45 of file order.hpp.

template<class View , bool Perm>
void Gecode::Int::Sorted::sort_tau ( ViewArray< View > &  x,
ViewArray< View > &  z,
int  tau[] 
) [inline]

Build $\tau$.

Creates a sorting permutation $\tau$ by sorting a given array of indices in tau according to the upper bounds of the views in x

Definition at line 74 of file order.hpp.

template<class View >
bool Gecode::Int::Sorted::normalize ( Space &  home,
ViewArray< View > &  y,
ViewArray< View > &  x,
bool &  nofix 
) [inline]

Performing normalization on the views in y.

The views in y are called normalized if $\forall i\in\{0,\dots, n-1\}: min(y_0) \leq \dots \leq min(y_{n-1}) \wedge max(y_0) \leq \dots \leq max(y_{n-1})$ holds.

Definition at line 93 of file order.hpp.

template<class View >
bool Gecode::Int::Sorted::perm_bc ( Space &  home,
int  tau[],
SccComponent  sinfo[],
int  scclist[],
ViewArray< View > &  x,
ViewArray< View > &  z,
bool &  crossingedge,
bool &  nofix 
) [inline]

Bounds consistency on the permutation views.

Check, whether the permutation view are bounds consistent. This function tests, whether there are "crossing edges", i.e. whether the current domains permit matchings between unsorted views x and the sorted variables y violating the property that y is sorted.

Definition at line 140 of file order.hpp.

template<class View , bool Perm>
ExecStatus Gecode::Int::Sorted::bounds_propagation ( Space &  home,
Propagator &  p,
ViewArray< View > &  x,
ViewArray< View > &  y,
ViewArray< View > &  z,
bool &  repairpass,
bool &  nofix,
bool &  match_fixed 
) [inline]

Perform bounds consistent sortedness propagation.

Implements the propagation algorithm for Sorted::Sorted and is provided as seperate function, because a second pass of the propagation algorithm is needed in order to achieve idempotency in case explicit permutation variables are provided.

If Perm is true, permutation variables form the third argument which implies additional inferences, consistency check on the permutation variables and eventually a second pass of the propagation algorithm. Otherwise, the algorithm does not take care of the permutation variables resulting in a better performance.

Definition at line 73 of file propagate.hpp.

template<class View , bool Perm>
bool Gecode::Int::Sorted::check_subsumption ( ViewArray< View > &  x,
ViewArray< View > &  y,
ViewArray< View > &  z,
bool &  subsumed,
int &  dropfst 
) [inline]

Subsumption test.

The propagator for sorted is subsumed if all variables of the ViewArrays x, y and z are determined and the constraint holds. In addition to the subsumption test check_subsumption determines, whether we can reduce the orginial problem to a smaller one, by dropping already matched variables.

Definition at line 78 of file sortsup.hpp.

template<class View , bool Perm>
bool Gecode::Int::Sorted::array_assigned ( Space &  home,
ViewArray< View > &  x,
ViewArray< View > &  y,
ViewArray< View > &  z,
bool &  subsumed,
bool &  match_fixed,
bool &  ,
bool &  noperm_bc 
) [inline]

Check for assignment of a variable array.

Check whether one of the argument arrays is completely assigned and udpates the other array respectively.

Definition at line 378 of file sortsup.hpp.

template<class View >
bool Gecode::Int::Sorted::channel ( Space &  home,
ViewArray< View > &  x,
ViewArray< View > &  y,
ViewArray< View > &  z,
bool &  nofix 
) [inline]

Channel between x, y and z.

Keep variables consisting by channeling information

Definition at line 489 of file sortsup.hpp.