File: graph.hh

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#ifndef BLISS_GRAPH_HH
#define BLISS_GRAPH_HH

/*
  Copyright (c) 2003-2015 Tommi Junttila
  Released under the GNU Lesser General Public License version 3.
  
  This file is part of bliss.
  
  bliss is free software: you can redistribute it and/or modify
  it under the terms of the GNU Lesser General Public License as published by
  the Free Software Foundation, version 3 of the License.

  bliss is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  GNU Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General Public License
  along with bliss.  If not, see <http://www.gnu.org/licenses/>.
*/

/**
 * \namespace bliss
 * The namespace bliss contains all the classes and functions of the bliss
 * tool except for the C programming language API.
 */
namespace bliss {
  class AbstractGraph;
}

#include <cstdio>
#include <vector>
#include <bliss/kstack.hh>
#include <bliss/kqueue.hh>
#include <bliss/heap.hh>
#include <bliss/orbit.hh>
#include <bliss/partition.hh>
#include <bliss/bignum.hh>
#include <bliss/uintseqhash.hh>

namespace bliss {

/**
 * \brief Statistics returned by the bliss search algorithm.
 */
class Stats
{
  friend class AbstractGraph;
  /** \internal The size of the automorphism group. */
  BigNum group_size;
  /** \internal An approximation (due to possible overflows) of
   * the size of the automorphism group. */
  long double group_size_approx;
  /** \internal The number of nodes in the search tree. */
  long unsigned int nof_nodes;
  /** \internal The number of leaf nodes in the search tree. */
  long unsigned int nof_leaf_nodes;
  /** \internal The number of bad nodes in the search tree. */
  long unsigned int nof_bad_nodes;
  /** \internal The number of canonical representative updates. */
  long unsigned int nof_canupdates;
  /** \internal The number of generator permutations. */
  long unsigned int nof_generators;
  /** \internal The maximal depth of the search tree. */
  unsigned long int max_level;
  /** */
  void reset()
  {
    group_size.assign(1);
    group_size_approx = 1.0;
    nof_nodes = 0;
    nof_leaf_nodes = 0;
    nof_bad_nodes = 0;
    nof_canupdates = 0;
    nof_generators = 0;
    max_level = 0;
  }
public:
  Stats() { reset(); }
  /** Print the statistics. */
  size_t print(FILE* const fp) const
  {
    size_t r = 0;
    r += fprintf(fp, "Nodes:          %lu\n", nof_nodes);
    r += fprintf(fp, "Leaf nodes:     %lu\n", nof_leaf_nodes);
    r += fprintf(fp, "Bad nodes:      %lu\n", nof_bad_nodes);
    r += fprintf(fp, "Canrep updates: %lu\n", nof_canupdates);
    r += fprintf(fp, "Generators:     %lu\n", nof_generators);
    r += fprintf(fp, "Max level:      %lu\n", max_level);
    r += fprintf(fp, "|Aut|:          ")+group_size.print(fp)+fprintf(fp, "\n");
    fflush(fp);
    return r;
  }
  /** An approximation (due to possible overflows/rounding errors) of
   * the size of the automorphism group. */
  long double get_group_size_approx() const {return group_size_approx;}
  /** The number of nodes in the search tree. */
  long unsigned int get_nof_nodes() const {return nof_nodes;}
  /** The number of leaf nodes in the search tree. */
  long unsigned int get_nof_leaf_nodes() const {return nof_leaf_nodes;}
  /** The number of bad nodes in the search tree. */
  long unsigned int get_nof_bad_nodes() const {return nof_bad_nodes;}
  /** The number of canonical representative updates. */
  long unsigned int get_nof_canupdates() const {return nof_canupdates;}
  /** The number of generator permutations. */
  long unsigned int get_nof_generators() const {return nof_generators;}
  /** The maximal depth of the search tree. */
  unsigned long int get_max_level() const {return max_level;}
};






/**
 * \brief An abstract base class for different types of graphs.
 */
class AbstractGraph
{
  friend class Partition;

public:
  AbstractGraph();
  virtual ~AbstractGraph();

  /**
   * Set the verbose output level for the algorithms.
   * \param level  the level of verbose output, 0 means no verbose output
   */
  void set_verbose_level(const unsigned int level);

  /**
   * Set the file stream for the verbose output.
   * \param fp  the file stream; if null, no verbose output is written
   */
  void set_verbose_file(FILE * const fp);

  /**
   * Add a new vertex with color \a color in the graph and return its index.
   */
  virtual unsigned int add_vertex(const unsigned int color = 0) = 0;

  /**
   * Add an edge between vertices \a source and \a target.
   * Duplicate edges between vertices are ignored but try to avoid introducing
   * them in the first place as they are not ignored immediately but will
   * consume memory and computation resources for a while.
   */
  virtual void add_edge(const unsigned int source, const unsigned int target) = 0;

  /**
   * Change the color of the vertex \a vertex to \a color.
   */
  virtual void change_color(const unsigned int vertex, const unsigned int color) = 0;

  /**
   * Check whether \a perm is an automorphism of this graph.
   * Unoptimized, mainly for debugging purposes.
   */
  virtual bool is_automorphism(const std::vector<unsigned int>& perm) const;


  /** Activate/deactivate failure recording.
   * May not be called during the search, i.e. from an automorphism reporting
   * hook function.
   * \param active  if true, activate failure recording, deactivate otherwise
   */
  void set_failure_recording(const bool active) {assert(!in_search); opt_use_failure_recording = active;}

  /** Activate/deactivate component recursion.
   * The choice affects the computed canonical labelings;
   * therefore, if you want to compare whether two graphs are isomorphic by
   * computing and comparing (for equality) their canonical versions,
   * be sure to use the same choice for both graphs.
   * May not be called during the search, i.e. from an automorphism reporting
   * hook function.
   * \param active  if true, activate component recursion, deactivate otherwise
   */
  void set_component_recursion(const bool active) {assert(!in_search); opt_use_comprec = active;}



  /**
   * Return the number of vertices in the graph.
   */
  virtual unsigned int get_nof_vertices() const = 0;

  /**
   * Return a new graph that is the result of applying the permutation \a perm
   * to this graph. This graph is not modified.
   * \a perm must contain N=this.get_nof_vertices() elements and be a bijection
   * on {0,1,...,N-1}, otherwise the result is undefined or a segfault.
   */
  virtual AbstractGraph* permute(const unsigned int* const perm) const = 0;
  virtual AbstractGraph* permute(const std::vector<unsigned int>& perm) const = 0;

  /**
   * Find a set of generators for the automorphism group of the graph.
   * The function \a hook (if non-null) is called each time a new generator
   * for the automorphism group is found.
   * The first argument \a user_param for the hook is the
   * \a hook_user_param given below,
   * the second argument \a n is the length of the automorphism (equal to
   * get_nof_vertices()) and
   * the third argument \a aut is the automorphism
   * (a bijection on {0,...,get_nof_vertices()-1}).
   * The memory for the automorphism \a aut will be invalidated immediately
   * after the return from the hook function;
   * if you want to use the automorphism later, you have to take a copy of it.
   * Do not call any member functions in the hook.
   * The search statistics are copied in \a stats.
   */
  void find_automorphisms(Stats& stats,
			  void (*hook)(void* user_param,
				       unsigned int n,
				       const unsigned int* aut),
			  void* hook_user_param);

  /**
   * Otherwise the same as find_automorphisms() except that
   * a canonical labeling of the graph (a bijection on
   * {0,...,get_nof_vertices()-1}) is returned.
   * The memory allocated for the returned canonical labeling will remain
   * valid only until the next call to a member function with the exception
   * that constant member functions (for example, bliss::Graph::permute()) can
   * be called without invalidating the labeling.
   * To compute the canonical version of an undirected graph, call this
   * function and then bliss::Graph::permute() with the returned canonical
   * labeling.
   * Note that the computed canonical version may depend on the applied version
   * of bliss as well as on some other options (for instance, the splitting
   * heuristic selected with bliss::Graph::set_splitting_heuristic()).
   */
  const unsigned int* canonical_form(Stats& stats,
				     void (*hook)(void* user_param,
						  unsigned int n,
						  const unsigned int* aut),
				     void* hook_user_param);

  /**
   * Write the graph to a file in a variant of the DIMACS format.
   * See the <A href="http://www.tcs.hut.fi/Software/bliss/">bliss website</A>
   * for the definition of the file format.
   * Note that in the DIMACS file the vertices are numbered from 1 to N while
   * in this C++ API they are from 0 to N-1.
   * Thus the vertex n in the file corresponds to the vertex n-1 in the API.
   * \param fp  the file stream where the graph is written
   */
  virtual void write_dimacs(FILE * const fp) = 0;

  /**
   * Write the graph to a file in the graphviz dotty format.
   * \param fp  the file stream where the graph is written
   */
  virtual void write_dot(FILE * const fp) = 0;

  /**
   * Write the graph in a file in the graphviz dotty format.
   * Do nothing if the file cannot be written.
   * \param file_name  the name of the file to which the graph is written
   */
  virtual void write_dot(const char * const file_name) = 0;

  /**
   * Get a hash value for the graph.
   * \return  the hash value
   */ 
  virtual unsigned int get_hash() = 0;

  /**
   * Disable/enable the "long prune" method.
   * The choice affects the computed canonical labelings;
   * therefore, if you want to compare whether two graphs are isomorphic by
   * computing and comparing (for equality) their canonical versions,
   * be sure to use the same choice for both graphs.
   * May not be called during the search, i.e. from an automorphism reporting
   * hook function.
   * \param active  if true, activate "long prune", deactivate otherwise
   */
  void set_long_prune_activity(const bool active) {
    assert(!in_search);
    opt_use_long_prune = active;
  }



protected:
  /** \internal
   * How much verbose output is produced (0 means none) */
  unsigned int verbose_level;
  /** \internal
   * The output stream for verbose output. */
  FILE *verbstr;
protected:

  /** \internal
   * The ordered partition used in the search algorithm. */
  Partition p;

  /** \internal
   * Whether the search for automorphisms and a canonical labeling is
   * in progress.
   */
  bool in_search;

  /** \internal
   * Is failure recording in use?
   */
  bool opt_use_failure_recording;
  /* The "tree-specific" invariant value for the point when current path
   * got different from the first path */
  unsigned int failure_recording_fp_deviation;

  /** \internal
   * Is component recursion in use?
   */
  bool opt_use_comprec;


  unsigned int refine_current_path_certificate_index;
  bool refine_compare_certificate;
  bool refine_equal_to_first;
  unsigned int refine_first_path_subcertificate_end;
  int refine_cmp_to_best;
  unsigned int refine_best_path_subcertificate_end;

  static const unsigned int CERT_SPLIT = 0; //UINT_MAX;
  static const unsigned int CERT_EDGE  = 1; //UINT_MAX-1;
  /** \internal
   * Add a triple (v1,v2,v3) in the certificate.
   * May modify refine_equal_to_first and refine_cmp_to_best.
   * May also update eqref_hash and failure_recording_fp_deviation. */
  void cert_add(const unsigned int v1,
		const unsigned int v2,
		const unsigned int v3);

  /** \internal
   * Add a redundant triple (v1,v2,v3) in the certificate.
   * Can also just dicard the triple.
   * May modify refine_equal_to_first and refine_cmp_to_best.
   * May also update eqref_hash and failure_recording_fp_deviation. */
  void cert_add_redundant(const unsigned int x,
			  const unsigned int y,
			  const unsigned int z);

  /**\internal
   * Is the long prune method in use?
   */
  bool opt_use_long_prune;
  /**\internal
   * Maximum amount of memory (in megabytes) available for
   * the long prune method
   */
  static const unsigned int long_prune_options_max_mem = 50;
  /**\internal
   * Maximum amount of automorphisms stored for the long prune method;
   * less than this is stored if the memory limit above is reached first
   */
  static const unsigned int long_prune_options_max_stored_auts = 100;

  unsigned int long_prune_max_stored_autss;
  std::vector<std::vector<bool> *> long_prune_fixed;
  std::vector<std::vector<bool> *> long_prune_mcrs;
  std::vector<bool> long_prune_temp;
  unsigned int long_prune_begin;
  unsigned int long_prune_end;
  /** \internal
   * Initialize the "long prune" data structures.
   */
  void long_prune_init();
  /** \internal
   * Release the memory allocated for "long prune" data structures.
   */
  void long_prune_deallocate();
  void long_prune_add_automorphism(const unsigned int *aut);
  std::vector<bool>& long_prune_get_fixed(const unsigned int index);
  std::vector<bool>& long_prune_allocget_fixed(const unsigned int index);
  std::vector<bool>& long_prune_get_mcrs(const unsigned int index);
  std::vector<bool>& long_prune_allocget_mcrs(const unsigned int index);
  /** \internal
   * Swap the i:th and j:th stored automorphism information;
   * i and j must be "in window, i.e. in [long_prune_begin,long_prune_end[
   */
  void long_prune_swap(const unsigned int i, const unsigned int j);

  /*
   * Data structures and routines for refining the partition p into equitable
   */
  Heap neighbour_heap;
  virtual bool split_neighbourhood_of_unit_cell(Partition::Cell *) = 0;
  virtual bool split_neighbourhood_of_cell(Partition::Cell * const) = 0;
  void refine_to_equitable();
  void refine_to_equitable(Partition::Cell * const unit_cell);
  void refine_to_equitable(Partition::Cell * const unit_cell1,
			   Partition::Cell * const unit_cell2);


  /** \internal
   * \return false if it was detected that the current certificate
   *         is different from the first and/or best (whether this is checked
   *         depends on in_search and refine_compare_certificate flags.
   */
  bool do_refine_to_equitable();

  unsigned int eqref_max_certificate_index;
  /** \internal
   * Whether eqref_hash is updated during equitable refinement process.
   */
  bool compute_eqref_hash;
  UintSeqHash eqref_hash;


  /** \internal
   * Check whether the current partition p is equitable.
   * Performance: very slow, use only for debugging purposes.
   */
  virtual bool is_equitable() const = 0;

  unsigned int *first_path_labeling;
  unsigned int *first_path_labeling_inv;
  Orbit         first_path_orbits;
  unsigned int *first_path_automorphism;

  unsigned int *best_path_labeling;
  unsigned int *best_path_labeling_inv;
  Orbit         best_path_orbits;
  unsigned int *best_path_automorphism;

  void update_labeling(unsigned int * const lab);
  void update_labeling_and_its_inverse(unsigned int * const lab,
				       unsigned int * const lab_inv);
  void update_orbit_information(Orbit &o, const unsigned int *perm);

  void reset_permutation(unsigned int *perm);

  /* Mainly for debugging purposes */
  virtual bool is_automorphism(unsigned int* const perm);

  std::vector<unsigned int> certificate_current_path;
  std::vector<unsigned int> certificate_first_path;
  std::vector<unsigned int> certificate_best_path;

  unsigned int certificate_index;
  virtual void initialize_certificate() = 0;

  virtual void remove_duplicate_edges() = 0;
  virtual void make_initial_equitable_partition() = 0;
  virtual Partition::Cell* find_next_cell_to_be_splitted(Partition::Cell *cell) = 0;


  void search(const bool canonical, Stats &stats);


  void (*report_hook)(void *user_param,
		      unsigned int n,
		      const unsigned int *aut);
  void *report_user_param;


  /*
   *
   * Nonuniform component recursion (NUCR)
   *
   */

  /** The currently traversed component */
  unsigned int cr_level;

  /** \internal
   * The "Component End Point" data structure
   */
  class CR_CEP {
  public:
    /** At which level in the search was this CEP created */
    unsigned int creation_level;
    /** The current component has been fully traversed when the partition has
     * this many discrete cells left */
    unsigned int discrete_cell_limit;
    /** The component to be traversed after the current one */
    unsigned int next_cr_level;
    /** The next component end point */
    unsigned int next_cep_index;
    bool first_checked;
    bool best_checked;
  };
  /** \internal
   * A stack for storing Component End Points
   */
  std::vector<CR_CEP> cr_cep_stack;

  /** \internal
   * Find the first non-uniformity component at the component recursion
   * level \a level.
   * The component is stored in \a cr_component.
   * If no component is found, \a cr_component is empty.
   * Returns false if all the cells in the component recursion level \a level
   * were discrete.
   * Modifies the max_ival and max_ival_count fields of Partition:Cell
   * (assumes that they are 0 when called and
   *  quarantees that they are 0 when returned).
   */
  virtual bool nucr_find_first_component(const unsigned int level) = 0;
  virtual bool nucr_find_first_component(const unsigned int level,
					 std::vector<unsigned int>& component,
					 unsigned int& component_elements,
					 Partition::Cell*& sh_return) = 0;
  /** \internal
   * The non-uniformity component found by nucr_find_first_component()
   * is stored here.
   */
  std::vector<unsigned int> cr_component;
  /** \internal
   * The number of vertices in the component \a cr_component
   */
  unsigned int cr_component_elements;




};



/**
 * \brief The class for undirected, vertex colored graphs.
 *
 * Multiple edges between vertices are not allowed (i.e., are ignored).
 */
class Graph : public AbstractGraph
{
public:
  /**
   * The possible splitting heuristics.
   * The selected splitting heuristics affects the computed canonical
   * labelings; therefore, if you want to compare whether two graphs
   * are isomorphic by computing and comparing (for equality) their
   * canonical versions, be sure to use the same splitting heuristics
   * for both graphs.
   */
  typedef enum {
    /** First non-unit cell.
     * Very fast but may result in large search spaces on difficult graphs.
     * Use for large but easy graphs. */
    shs_f = 0,
    /** First smallest non-unit cell.
     * Fast, should usually produce smaller search spaces than shs_f. */
    shs_fs,
    /** First largest non-unit cell.
     * Fast, should usually produce smaller search spaces than shs_f. */
    shs_fl,
    /** First maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_fm,
    /** First smallest maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_fsm,
    /** First largest maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_flm
  } SplittingHeuristic;

protected:
  class Vertex {
  public:
    Vertex();
    ~Vertex();
    void add_edge(const unsigned int other_vertex);
    void remove_duplicate_edges(std::vector<bool>& tmp);
    void sort_edges();

    unsigned int color;
    std::vector<unsigned int> edges;
    unsigned int nof_edges() const {return edges.size(); }
  };
  std::vector<Vertex> vertices;
  void sort_edges();
  void remove_duplicate_edges();

  /** \internal
   * Partition independent invariant.
   * Returns the color of the vertex.
   * Time complexity: O(1).
   */
  static unsigned int vertex_color_invariant(const Graph* const g,
					     const unsigned int v);
  /** \internal
   * Partition independent invariant.
   * Returns the degree of the vertex.
   * DUPLICATE EDGES MUST HAVE BEEN REMOVED BEFORE.
   * Time complexity: O(1).
   */
  static unsigned int degree_invariant(const Graph* const g,
				       const unsigned int v);
  /** \internal
   * Partition independent invariant.
   * Returns 1 if there is an edge from the vertex to itself, 0 if not.
   * Time complexity: O(k), where k is the number of edges leaving the vertex.
   */
  static unsigned int selfloop_invariant(const Graph* const g,
					 const unsigned int v);


  bool refine_according_to_invariant(unsigned int (*inv)(const Graph* const g,
							 const unsigned int v));

  /*
   * Routines needed when refining the partition p into equitable
   */
  bool split_neighbourhood_of_unit_cell(Partition::Cell *);
  bool split_neighbourhood_of_cell(Partition::Cell * const);

  /** \internal
   * \copydoc AbstractGraph::is_equitable() const
   */
  bool is_equitable() const;

  /* Splitting heuristics, documented in more detail in graph.cc */
  SplittingHeuristic sh;
  Partition::Cell* find_next_cell_to_be_splitted(Partition::Cell *cell);
  Partition::Cell* sh_first();
  Partition::Cell* sh_first_smallest();
  Partition::Cell* sh_first_largest();
  Partition::Cell* sh_first_max_neighbours();
  Partition::Cell* sh_first_smallest_max_neighbours();
  Partition::Cell* sh_first_largest_max_neighbours();


  void make_initial_equitable_partition();

  void initialize_certificate();
  
  bool is_automorphism(unsigned int* const perm);


  bool nucr_find_first_component(const unsigned int level);
  bool nucr_find_first_component(const unsigned int level,
				 std::vector<unsigned int>& component,
				 unsigned int& component_elements,
				 Partition::Cell*& sh_return);



public:
  /**
   * Create a new graph with \a N vertices and no edges.
   */
  Graph(const unsigned int N = 0);

  /**
   * Destroy the graph.
   */
  ~Graph();

  /**
   * Read the graph from the file \a fp in a variant of the DIMACS format.
   * See the <A href="http://www.tcs.hut.fi/Software/bliss/">bliss website</A>
   * for the definition of the file format.
   * Note that in the DIMACS file the vertices are numbered from 1 to N while
   * in this C++ API they are from 0 to N-1.
   * Thus the vertex n in the file corresponds to the vertex n-1 in the API.
   *
   * \param fp      the file stream for the graph file
   * \param errstr  if non-null, the possible error messages are printed
   *                in this file stream
   * \return        a new Graph object or 0 if reading failed for some
   *                reason
   */
  static Graph* read_dimacs(FILE* const fp, FILE* const errstr = stderr);

  /**
   * Write the graph to a file in a variant of the DIMACS format.
   * See the <A href="http://www.tcs.hut.fi/Software/bliss/">bliss website</A>
   * for the definition of the file format.
   */
  void write_dimacs(FILE* const fp);

  /**
   * \copydoc AbstractGraph::write_dot(FILE * const fp)
   */
  void write_dot(FILE* const fp);

  /**
   * \copydoc AbstractGraph::write_dot(const char * const file_name)
   */
  void write_dot(const char* const file_name);

  /**
   * \copydoc AbstractGraph::is_automorphism(const std::vector<unsigned int>& perm) const
   */
  bool is_automorphism(const std::vector<unsigned int>& perm) const;


  /**
   * \copydoc AbstractGraph::get_hash()
   */ 
  virtual unsigned int get_hash();

  /**
   * Return the number of vertices in the graph.
   */
  unsigned int get_nof_vertices() const {return vertices.size(); }

  /**
   * \copydoc AbstractGraph::permute(const unsigned int* const perm) const
   */
  Graph* permute(const unsigned int* const perm) const;
  Graph* permute(const std::vector<unsigned int>& perm) const;
  
  /**
   * Add a new vertex with color \a color in the graph and return its index.
   */
  unsigned int add_vertex(const unsigned int color = 0);

  /**
   * Add an edge between vertices \a v1 and \a v2.
   * Duplicate edges between vertices are ignored but try to avoid introducing
   * them in the first place as they are not ignored immediately but will
   * consume memory and computation resources for a while.
   */
  void add_edge(const unsigned int v1, const unsigned int v2);

  /**
   * Change the color of the vertex \a vertex to \a color.
   */
  void change_color(const unsigned int vertex, const unsigned int color);

  /**
   * Compare this graph with the graph \a other.
   * Returns 0 if the graphs are equal, and a negative (positive) integer
   * if this graph is "smaller than" ("greater than", resp.) than \a other.
   */
  int cmp(Graph& other);

  /**
   * Set the splitting heuristic used by the automorphism and canonical
   * labeling algorithm.
   * The selected splitting heuristics affects the computed canonical
   * labelings; therefore, if you want to compare whether two graphs
   * are isomorphic by computing and comparing (for equality) their
   * canonical versions, be sure to use the same splitting heuristics
   * for both graphs.
   */
  void set_splitting_heuristic(const SplittingHeuristic shs) {sh = shs; }
  

};



/**
 * \brief The class for directed, vertex colored graphs.
 *
 * Multiple edges between vertices are not allowed (i.e., are ignored).
 */
class Digraph : public AbstractGraph
{
public:
  /**
   * The possible splitting heuristics.
   * The selected splitting heuristics affects the computed canonical
   * labelings; therefore, if you want to compare whether two graphs
   * are isomorphic by computing and comparing (for equality) their
   * canonical versions, be sure to use the same splitting heuristics
   * for both graphs.
   */
  typedef enum {
    /** First non-unit cell.
     * Very fast but may result in large search spaces on difficult graphs.
     * Use for large but easy graphs. */
    shs_f = 0,
    /** First smallest non-unit cell.
     * Fast, should usually produce smaller search spaces than shs_f. */
    shs_fs,
    /** First largest non-unit cell.
     * Fast, should usually produce smaller search spaces than shs_f. */
    shs_fl,
    /** First maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_fm,
    /** First smallest maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_fsm,
    /** First largest maximally non-trivially connected non-unit cell.
     * Not so fast, should usually produce smaller search spaces than shs_f,
     * shs_fs, and shs_fl. */
    shs_flm
  } SplittingHeuristic;

protected:
  class Vertex {
  public:
    Vertex();
    ~Vertex();
    void add_edge_to(const unsigned int dest_vertex);
    void add_edge_from(const unsigned int source_vertex);
    void remove_duplicate_edges(std::vector<bool>& tmp);
    void sort_edges();
    unsigned int color;
    std::vector<unsigned int> edges_out;
    std::vector<unsigned int> edges_in;
    unsigned int nof_edges_in() const {return edges_in.size(); }
    unsigned int nof_edges_out() const {return edges_out.size(); }
  };
  std::vector<Vertex> vertices;
  void remove_duplicate_edges();

  /** \internal
   * Partition independent invariant.
   * Returns the color of the vertex.
   * Time complexity: O(1).
   */
  static unsigned int vertex_color_invariant(const Digraph* const g,
					     const unsigned int v);
  /** \internal
   * Partition independent invariant.
   * Returns the indegree of the vertex.
   * DUPLICATE EDGES MUST HAVE BEEN REMOVED BEFORE.
   * Time complexity: O(1).
   */
  static unsigned int indegree_invariant(const Digraph* const g,
					 const unsigned int v);
  /** \internal
   * Partition independent invariant.
   * Returns the outdegree of the vertex.
   * DUPLICATE EDGES MUST HAVE BEEN REMOVED BEFORE.
   * Time complexity: O(1).
   */
  static unsigned int outdegree_invariant(const Digraph* const g,
					  const unsigned int v);
  /** \internal
   * Partition independent invariant.
   * Returns 1 if there is an edge from the vertex to itself, 0 if not.
   * Time complexity: O(k), where k is the number of edges leaving the vertex.
   */
  static unsigned int selfloop_invariant(const Digraph* const g,
					 const unsigned int v);

  /** \internal
   * Refine the partition \a p according to
   * the partition independent invariant \a inv.
   */
  bool refine_according_to_invariant(unsigned int (*inv)(const Digraph* const g,
							 const unsigned int v));

  /*
   * Routines needed when refining the partition p into equitable
   */
  bool split_neighbourhood_of_unit_cell(Partition::Cell* const);
  bool split_neighbourhood_of_cell(Partition::Cell* const);


  /** \internal
   * \copydoc AbstractGraph::is_equitable() const
   */
  bool is_equitable() const;

  /* Splitting heuristics, documented in more detail in the cc-file. */
  SplittingHeuristic sh;
  Partition::Cell* find_next_cell_to_be_splitted(Partition::Cell *cell);
  Partition::Cell* sh_first();
  Partition::Cell* sh_first_smallest();
  Partition::Cell* sh_first_largest();
  Partition::Cell* sh_first_max_neighbours();
  Partition::Cell* sh_first_smallest_max_neighbours();
  Partition::Cell* sh_first_largest_max_neighbours();

  void make_initial_equitable_partition();

  void initialize_certificate();

  bool is_automorphism(unsigned int* const perm);

  void sort_edges();

  bool nucr_find_first_component(const unsigned int level);
  bool nucr_find_first_component(const unsigned int level,
				 std::vector<unsigned int>& component,
				 unsigned int& component_elements,
				 Partition::Cell*& sh_return);

public:
  /**
   * Create a new directed graph with \a N vertices and no edges.
   */
  Digraph(const unsigned int N = 0);

  /**
   * Destroy the graph.
   */
  ~Digraph();

  /**
   * Read the graph from the file \a fp in a variant of the DIMACS format.
   * See the <A href="http://www.tcs.hut.fi/Software/bliss/">bliss website</A>
   * for the definition of the file format.
   * Note that in the DIMACS file the vertices are numbered from 1 to N while
   * in this C++ API they are from 0 to N-1.
   * Thus the vertex n in the file corresponds to the vertex n-1 in the API.
   * \param fp      the file stream for the graph file
   * \param errstr  if non-null, the possible error messages are printed
   *                in this file stream
   * \return        a new Digraph object or 0 if reading failed for some
   *                reason
   */
  static Digraph* read_dimacs(FILE* const fp, FILE* const errstr = stderr);

  /**
   * \copydoc AbstractGraph::write_dimacs(FILE * const fp)
   */
  void write_dimacs(FILE* const fp);


  /**
   * \copydoc AbstractGraph::write_dot(FILE *fp)
   */
  void write_dot(FILE * const fp);

  /**
   * \copydoc AbstractGraph::write_dot(const char * const file_name)
   */
  void write_dot(const char * const file_name);

  /**
   * \copydoc AbstractGraph::is_automorphism(const std::vector<unsigned int>& perm) const
   */
  bool is_automorphism(const std::vector<unsigned int>& perm) const;



  /**
   * \copydoc AbstractGraph::get_hash()
   */ 
  virtual unsigned int get_hash();

  /**
   * Return the number of vertices in the graph.
   */
  unsigned int get_nof_vertices() const {return vertices.size(); }
  
  /**
   * Add a new vertex with color 'color' in the graph and return its index.
   */
  unsigned int add_vertex(const unsigned int color = 0);

  /**
   * Add an edge from the vertex \a source to the vertex \a target.
   * Duplicate edges are ignored but try to avoid introducing
   * them in the first place as they are not ignored immediately but will
   * consume memory and computation resources for a while.
   */
  void add_edge(const unsigned int source, const unsigned int target);

  /**
   * Change the color of the vertex 'vertex' to 'color'.
   */
  void change_color(const unsigned int vertex, const unsigned int color);

  /**
   * Compare this graph with the graph \a other.
   * Returns 0 if the graphs are equal, and a negative (positive) integer
   * if this graph is "smaller than" ("greater than", resp.) than \a other.
   */
  int cmp(Digraph& other);

  /**
   * Set the splitting heuristic used by the automorphism and canonical
   * labeling algorithm.
   * The selected splitting heuristics affects the computed canonical
   * labelings; therefore, if you want to compare whether two graphs
   * are isomorphic by computing and comparing (for equality) their
   * canonical versions, be sure to use the same splitting heuristics
   * for both graphs.
   */
  void set_splitting_heuristic(SplittingHeuristic shs) {sh = shs; }

  /**
   * \copydoc AbstractGraph::permute(const unsigned int* const perm) const
   */
  Digraph* permute(const unsigned int* const perm) const;  
  Digraph* permute(const std::vector<unsigned int>& perm) const;
};




}

#endif