MutableGraph

MutableGraph

A MutableGraph can be changed via the addition or removal of edges and vertices.

Refinement of

Notation

`G`	A type that is a model of Graph.
`g`	An object of type `G`.
`e`	An object of type `boost::graph_traits<G>::edge_descriptor`.
`u,v`	are objects of type `boost::graph_traits<G>::vertex_descriptor`.

Valid Expressions

Name	Expression	Return Type	Description
Add Edge	`add_edge(g, u, v)`	`std::pair<edge_descriptor, bool>`	Inserts the edge (u,v) into the graph.
Remove Edge	`remove_edge(g, u, v)`	`void`	Remove the edge (u,v) from the graph. If the graph allows parallel edges this remove all occurances of (u,v). Precondition: u and v are vertices in the graph. Postcondition: (u,v) is no longer in the edge set for `g`.
Remove Edge	`remove_edge(g, e)`	`void`	Remove the edge e from the graph. Precondition: e is an edge in the graph. Postcondition: e is no longer in the edge set for `g`.
Add Vertex	`add_vertex(g)`	`vertex_descriptor`	Add a new vertex to the graph. The `vertex_descriptor` for the new vertex is returned.
Clear Vertex	`clear_vertex(g, u)`	`void`	Remove all edges to and from vertex `u` from the graph. Precondition: `u` is a valid vertex descriptor of `g`. Postcondition: `u` does not appear as a source or target of any edge in `g`.
Remove Vertex	`remove_vertex(g, u)`	`void`	Remove u from the vertex set of the graph. Note that undefined behaviour may result if there are edges remaining in the graph who's target is u. Typically the `clear_vertex()` function should be called first. Precondition: `u` is a valid vertex descriptor of `g`. Postcondition: `num_vertices(g)` is one less, `u` no longer appears in the vertex set of the graph and it is no longer a valid vertex descriptor.

Complexity Guarantees

Edge insertion must be either amortized constant time or it can be O(log(E/V)) if the insertion also checks to prevent the addition of parallel edges (which is a ``feature'' of some graph types).
Edge removal is guaranteed to be O(E).
Vertex insertion is guaranteed to be amortized constant time.
Clearing a vertex is O(E + V).
Vertex removal is O(E + V).

Models

adjacency_list

Concept Checking Class

  template <class G>
  struct MutableGraph_concept
  {
    typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
    void constraints() {
      v = add_vertex(g);
      clear_vertex(g, v);
      remove_vertex(g, v);
      p = add_edge(g, u, v);
      remove_edge(g, u, v);
      remove_edge(g, e);
    }
    G g;
    edge_descriptor e;
    std::pair<edge_descriptor, bool> p;
    typename boost::graph_traits<G>::vertex_descriptor u, v;
  };

Jeremy Siek, Univ.of Notre Dame (jsiek@lsc.nd.edu)