# `maximum_adjacency_search`

    // named parameter versions
    template <class Graph, class class P, class T, class R>
    void
    maximum_adjacency_search(const Graph& g,
           const bgl_named_params<P, T, R>& params);

    // non-named parameter versions
    template <class Graph, class WeightMap, class MASVisitor>
    void
    maximum_adjacency_search(const Graph& g, WeightMap weights, MASVisitor vis,
           const typename graph_traits<Graph>::vertex_descriptor start);

The `maximum_adjacency_search()` function performs a traversal of the vertices in an undirected graph. The next vertex visited is the vertex that has the most visited neighbors at any time. In the case of an unweighted, undirected graph, the number of visited neighbors of the very last vertex visited in the graph is also the number of edge-disjoint paths between that vertex and the next-to-last vertex visited. These can be retrieved from a visitor, an example of which is in the test harness mas_test.cpp.

The `maximum_adjacency_search()` function invokes user-defined actions at certain event-points within the algorithm. This provides a mechanism for adapting the generic MAS algorithm to the many situations in which it can be used. In the pseudo-code below, the event points for MAS are the labels on the right. The user-defined actions must be provided in the form of a visitor object, that is, an object whose type meets the requirements for a MAS Visitor.

    MAS(G)
      for each vertex u in V
        reach_count[u] := 0
      end for
      // for the starting vertex s
      reach_count[s] := 1
      for each unvisited vertex u in V
        call MAS-VISIT(G, u)
        remove u from the list on unvisited vertices
        for each out edge from u to t
           if t has not yet been visited
             increment reach_count[t]
           end if
        end for each out edge
        call MAS-VISIT(G, u)
      end for each unvisited vertex
    -
    -
    initialize vertex u
    -
    -
    -
    -
    examine vertex u
    -
    examine edge (u,t)
    -
    -
    -
    -
    finish vertex u
    -

### Where Defined

`boost/graph/maximum_adjacency_search.hpp`

### Parameters

IN: `const UndirectedGraph& g`

> A connected, directed graph. The graph type must be a model of Incidence Graph and Vertex List Graph.

### Named Parameters

IN: `WeightMap weights`

> The weight or length of each edge in the graph. The `WeightMap` type must be a model of Readable Property Map and its value type must be Less Than Comparable and summable. The key type of this map needs to be the graph's edge descriptor type. Default: `get(edge_weight, g)`

IN: `visitor(MASVisitor vis)`

> A visitor object that is invoked inside the algorithm at the event-points specified by the MAS Visitor concept. The visitor object is passed by value [1].
> Default: `mas_visitor<null_visitor>`

IN: `root_vertex(typename graph_traits<VertexListGraph>::vertex_descriptor start)`

> This specifies the vertex that the depth-first search should originate from. The type is the type of a vertex descriptor for the given graph.
> Default: `*vertices(g).first`

#### Expert Parameters

IN: `vertex_index_map(VertexIndexMap vertexIndices)`

> This maps each vertex to an integer in the range [0, `num_vertices(g)`). This is only necessary if the default is used for the assignment, index-in-heap, or distance maps. `VertexIndexMap` must be a model of Readable Property Map. The value type of the map must be an integer type. The key type must be the graph's vertex descriptor type.
> Default: `get(boost::vertex_index, g)` Note: if you use this default, make sure your graph has an internal `vertex_index` property. For example, `adjacency_list` with `VertexList=listS` does not have an internal `vertex_index` property.

UTIL: `vertex_assignment_map(AssignmentMap assignments)`

> `AssignmentMap` must be a model of Read/Write Property Map. The key and value types must be the graph's vertex descriptor type.
> Default: A `boost::iterator_property_map` using a `std::vector` of `num_vertices(g)` vertex descriptors and `vertexIndices` for the index map.

UTIL: `max_priority_queue(MaxPriorityQueue& pq)`

> `MaxPriorityQueue` must be a model of Keyed Updatable Queue and a max- Updatable Priority Queue. The value type must be the graph's vertex descriptor and the key type must be the weight type. Default: A `boost::d_ary_heap_indirect` using a default index-in-heap and distance map.

UTIL: `index_in_heap_map(IndexInHeapMap indicesInHeap)`

> This parameter only has an effect when the default max-priority queue is used.
> `IndexInHeapMap` must be a model of Read/Write Property Map. The key type must be the graph's vertex descriptor type. The value type must be a size type (`typename std::vector<vertex_descriptor>::size_type`).
> Default: A `boost::iterator_property_map` using a `std::vector` of `num_vertices(g)` size type objects and `vertexIndices` for the index map.

UTIL: `distance_map(DistanceMap wAs)`

> This parameter only has an effect when the default max-priority queue is used.
> `DistanceMap` must be a model of Read/Write Property Map. The key type must be the graph's vertex descriptor type. The value type must be the weight type (`typename boost::property_traits<WeightMap>::value_type`).
> Default: A `boost::iterator_property_map` using a `std::vector` of `num_vertices(g)` weight type objects and `vertexIndices` for the index map.

### Returns

void

### Throws

`bad_graph`

> If `num_vertices(g)` is less than 2

`std::invalid_argument`

> If a max-priority queue is given as an argument and it is not empty

.

### Complexity

The time complexity is O(E + V).

### References

- David Matula (1993). A linear time 2 + epsilon approximation algorightm for edge connectivity
- Cai, Weiqing and Matula, David W. Partitioning by maximum adjacency search of graphs. Partitioning Data Sets: Dimacs Workshop, April 19-21, 1993. Vol 19. Page 55. 1995. Amer Mathematical Society
}

### Visitor Event Points

- `vis.initialize_vertex(s, g)` is invoked on every vertex of the graph before the start of the graph search.
- `vis.start_vertex(s, g)` is invoked on the source vertex once before processing its out edges.
- `vis.examine_edge(e, g)` is invoked on every out-edge of each vertex after it is started.
- `vis.finish_vertex(u, g)` is invoked on a vertex after all of its out edges have been examined and the reach counts of the unvisited targets have been updated.

### Notes

[1] Since the visitor parameter is passed by value, if your visitor contains state then any changes to the state during the algorithm will be made to a copy of the visitor object, not the visitor object passed in. Therefore you may want the visitor to hold this state by pointer or reference.

Copyright © 2012 | Fernando Vilas