Property Maps

The main link between the abstract mathematical nature of graphs and the concrete problems they are used to solve is the properties that are attached to the vertices and edges of a graph, things like distance, capacity, weight, color, etc. There are many ways to attach properties to graph in terms of data-structure implementation, but graph algorithms should not have to deal with the implementation details of the properties. The property map interface defined in Section Property Map Concepts provides a generic method for accessing properties from graphs. This is the interface used in the BGL algorithms to access properties.

Property Map Interface

The property map interface specifies that each property is accessed using a separate property map object. In the following example we show an implementation of the relax() function used inside of Dijkstra's shortest paths algorithm. In this function, we need to access the weight property of an edge, and the distance property of a vertex. We write relax() as a template function so that it can be used in many difference situations. Two of the arguments to the function, weight and distance, are the property map objects. In general, BGL algorithms explicitly pass property map objects for every property that a function will need. The property map interface defines several functions, two of which we use here: get() and put(). The get() function takes a property map object, such as distance and a key object. In the case of the distance property we are using the vertex objects u and v as keys. The get() function then returns the property value for the vertex.

  template <class Edge, class Graph,
            class WeightPropertyMap, 
            class DistancePropertyMap>
  bool relax(Edge e, const Graph& g, 
             WeightPropertyMap weight, 
             DistancePropertyMap distance)
  {
    typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
    Vertex u = source(e,g), v = target(e,g);
    if ( get(distance, u) + get(weight, e) < get(distance, v)) {
      put(distance, v, get(distance, u) + get(weight, e));
      return true;
    } else
      return false;
  }

Similar to the iterator_traits class of the STL, there is a property_traits class that can be used to deduce the types associated with a property map type: the key and value types, and the property map category (which is used to tell whether the map is readable, writeable, or both). In the relax() function we could have used property_traits to declare local variables of the distance property type.

  {
    typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
    Vertex u = source(e,g), v = target(e,g);
    typename property_traits<DistancePropertyMap>::value_type
      du, dv; // local variables of the distance property type
    du = get(distance, u);
    dv = get(distance, v);
    if (du + get(weight, e) < dv) {
      put(distance, v, du + get(weight, e));
      return true;
    } else
      return false;
  }

There are two kinds of graph properties: interior and exterior.

Interior Properties

are stored ``inside'' the graph object in some way, and the lifetime of the property value objects is the same as that of the graph object.

Exterior Properties

are stored ``outside'' of the graph object and the lifetime of the property value objects is independent of the graph. This is useful for properties that are only needed temporarily, perhaps for the duration of a particular algorithm such as the color property used in breadth_first_search(). When using exterior properties with a BGL algorithm a property map object for the exterior property must be passed as an argument to the algorithm.

Interior Properties

A graph type that supports interior property storage (such as adjacency_list) provides access to its property map objects through the interface defined in PropertyGraph. There is a function get(Property, g) that get property map objects from a graph. The first argument is the property type to specify which property you want to access and the second argument is the graph object. A graph type must document which properties (and therefore tags) it provides access to. The type of the property map depends on the type of graph and the property being mapped. A trait class is defined that provides a generic way to deduce the property map type: property_map. The following code shows how one can obtain the property map for the distance and weight properties of some graph type.

  property_map<Graph, vertex_distance_t>::type d
    = get(vertex_distance, g);

  property_map<Graph, edge_weight_t>::type w
    = get(edge_weight, g);

In general, the BGL algorithms require all property maps needed by the algorithm to be explicitly passed to the algorithm. For example, the BGL Dijkstra's shortest paths algorithm requires four property maps: distance, weight, color, and vertex ID.

Often times some or all of the properties will be interior to the graph, so one would call Dijkstra's algorithm in the following way (given some graph g and source vertex src).

  dijkstra_shortest_paths(g, src,  
    distance_map(get(vertex_distance, g)).
    weight_map(get(edge_weight, g)).
    color_map(get(vertex_color, g)).
    vertex_index_map(get(vertex_index, g)));

Since it is somewhat cumbersome to specify all of the property maps, BGL provides defaults that assume some of the properties are interior and can be accessed via get(Property, g) from the graph, or if the property map is only used internally, then the algorithm will create a property map for itself out of an array and using the graph's vertex index map as the offset into the array. Below we show a call to dijkstra_shortest_paths algorithm using all defaults for the named parameters. This call is equivalent to the previous call to Dijkstra's algorithm.

  dijkstra_shortest_paths(g, src);

The next question is: how do interior properties become attached to a graph object in the first place? This depends on the graph class that you are using. The adjacency_list graph class of BGL uses a property mechanism (see Section Internal Properties) to allow an arbitrary number of properties to be stored on the edges and vertices of the graph.

Exterior Properties

In this section we will describe two methods for constructing exterior property maps, however there is an unlimited number of ways that one could create exterior properties for a graph.

The first method uses the adaptor class random_access_iterator_property_map. This class wraps a random access iterator, creating a property map out of it. The random access iterator must point to the beginning of a range of property values, and the length of the range must be the number of vertices or edges in the graph (depending on whether it is a vertex or edge property map). The adaptor must also be supplied with an ID property map, which will be used to map the vertex or edge descriptor to the offset of the property value (offset from the random access iterator). The ID property map will typically be an interior property map of the graph. The following example shows how the random_access_iterator_property_map can be used to create exterior property maps for the capacity and flow properties, which are stored in arrays. The arrays are indexed by edge ID. The edge ID is added to the graph using a property, and the values of the ID's are given when each edge is added to the graph. The complete source code for this example is in example/exterior_edge_properties.cpp. The print_network() function prints out the graph with the flow and capacity values.

  typedef adjacency_list<vecS, vecS, bidirectionalS, 
    no_property, property<edge_index_t, std::size_t> > Graph;

  const int num_vertices = 9;
  Graph G(num_vertices);

  int capacity_array[] = { 10, 20, 20, 20, 40, 40, 20, 20, 20, 10 };
  int flow_array[] = { 8, 12, 12, 12, 12, 12, 16, 16, 16, 8 };

  // Add edges to the graph, and assign each edge an ID number.
  add_edge(0, 1, 0, G);
  // ...

  typedef graph_traits<Graph>::edge_descriptor Edge;
  typedef property_map<Graph, edge_index_t>::type EdgeID_Map;
  EdgeID_Map edge_id = get(edge_index, G);

  random_access_iterator_property_map
    <int*, int, int&, EdgeID_Map> 
      capacity(capacity_array, edge_id), 
      flow(flow_array, edge_id);

  print_network(G, capacity, flow);

The second method uses a pointer type (a pointer to an array of property values) as a property map. This requires the key type to be an integer so that it can be used as an offset to the pointer. The adjacency_list class with template parameter VertexList=vecS uses integers for vertex descriptors (indexed from zero to the number of vertices in the graph), so they are suitable as the key type for a pointer property map. When the VertexList is not vecS, then the vertex descriptor is not an integer, and cannot be used with a pointer property map. Instead the method described above of using a random_access_iterator_property_map with an ID property must be used. The edge_list class may also use an integer type for the vertex descriptor, depending on how the adapted edge iterator is defined. The example in example/bellman_ford.cpp shows edge_list being used with pointers as vertex property maps.

The reason that pointers can be used as property maps is that there are several overloaded functions and a specialization of property_traits in the header boost/property_map.hpp that implement the property map interface in terms of pointers. The definition of those functions is listed here.

namespace boost {
  template <class T>
  struct property_traits<T*> {
    typedef T value_type;
    typedef ptrdiff_t key_type;
    typedef lvalue_property_map_tag category;
  };

  template <class T>
  void put(T* pa, std::ptrdiff_t key, const T& value) { pa[key] = value;  }

  template <class T>
  const T& get(const T* pa, std::ptrdiff_t key) { return pa[key]; }

  template <class T>
  const T& at(const T* pa, std::ptrdiff_t key) { return pa[key]; }

  template <class T>
  T& at(T* pa, std::ptrdiff_t key) { return pa[key]; }
}

In the following example, we use an array to store names of cities for each vertex in the graph, and a std::vector to store vertex colors which will be needed in a call to breadth_first_search(). Since the iterator of a std::vector (obtained with a call to begin()) is a pointer, the pointer property map method also works for std::vector::iterator. The complete source code for this example is in example/city_visitor.cpp.

// Definition of city_visitor omitted...

int main(int,char*[])
{
  enum { SanJose, SanFran, LA, SanDiego, Fresno, LosVegas, Reno,
         Sacramento, SaltLake, Pheonix, N };

  // An array of vertex name properties
  std::string names[] = { "San Jose", "San Francisco",  "San Jose",
                          "San Francisco", "Los Angeles", "San Diego", 
                          "Fresno", "Los Vegas", "Reno", "Sacramento",
                          "Salt Lake City", "Pheonix" };

  // Specify all the connecting roads between cities.
  typedef std::pair<int,int> E;
  E edge_array[] = { E(Sacramento, Reno), ... };

  // Specify the graph type.
  typedef adjacency_list<vecS, vecS, undirectedS> Graph;
  // Create the graph object, based on the edges in edge_array.
  Graph G(N, edge_array, edge_array + sizeof(edge_array)/sizeof(E));

  // DFS and BFS need to "color" the vertices.
  // Here we use std::vector as exterior property storage.
  std::vector<default_color_type> colors(N);

  cout << "*** Depth First ***" << endl;
  depth_first_search(G, city_visitor(names), colors.begin());
  cout << endl;

  // Get the source vertex
  boost::graph_traits<Graph>::vertex_descriptor 
    s = vertex(SanJose, G);

  cout << "*** Breadth First ***" << endl;
  breadth_first_search(G, s, city_visitor(names), colors.begin());

  return 0;
}

Constructing an Exterior Property Map

Implementing your own exterior property maps is not very difficult. You simply need to overload the functions required by the property map concept that you want your class to model. At most, this means overloading the put() and get() functions and implementing operator[]. Also, your property map class will need to have nested typedefs for all the types defined in property_traits, or you can create a specialization of property_traits for your new property map type.

The implementation of the random_access_iterator_property_map class serves as a good example for how to build and exterior property map. Here we present a simplified implementation of the random_access_iterator_property_map class which we will name iterator_pa.

We start with the definition of the iterator_map class itself. This adaptor class is templated on the adapted Iterator type and the ID property map. The job of the ID property map is to map the key object (which will typically be a vertex or edge descriptor) to an integer offset. The iterator_map class will need the three necessary typedefs for a property map: key_type, value_type, and category. We can use property_traits to find the key type of IDMap, and we can use iterator_traits to determine the value type of Iterator. We choose boost::lvalue_property_map_tag for the category since we plan on implementing the at() function.

  template <class Iterator, class IDMap>
  class iterator_map
  {
  public:
    typedef typename boost::property_traits<IDMap>::key_type key_type; 
    typedef typename std::iterator_traits<Iterator>::value_type value_type;
    typedef boost::lvalue_property_map_tag category;

    iterator_map(Iterator i = Iterator(), 
                const IDMap& id = IDMap()) 
      : m_iter(i), m_id(id) { }
    Iterator m_iter;
    IDMap m_id;
  };

Next we implement the three property map functions, get(), put(), and at(). In each of the functions, the key object is converted to an integer offset using the m_id property map, and then that is used as an offset to the random access iterator m_iter.

  template <class Iter, class ID>
  typename std::iterator_traits<Iter>::value_type
  get(const iterator_map<Iter,ID>& i,
      typename boost::property_traits<ID>::key_type key)
  {
    return i.m_iter[i.m_id[key]];
  }
  template <class Iter, class ID>
  void
  put(const iterator_map<Iter,ID>& i,
      typename boost::property_traits<ID>::key_type key,
      const typename std::iterator_traits<Iter>::value_type& value)
  {
    i.m_iter[i.m_id[key]] = value;
  }
  template <class Iter, class ID>
  typename std::iterator_traits<Iter>::reference
  at(const iterator_map<Iter,ID>& i,
      typename boost::property_traits<ID>::key_type key)
  {
    return i.m_iter[i.m_id[key]];
  }

That is it. The iterator_map class is complete and could be used just like the random_access_iterator_property_map in the previous section.