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regarded and expertly designed C++ library projects in the
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— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

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.

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; }The function

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.

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.

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
`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 `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); 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
`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/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; }

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
`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
`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
`iterator_property_map` in the
previous section.

Copyright © 2000-2001 | Jeremy Siek, Indiana University (jsiek@osl.iu.edu) |