+++ /dev/null
-.. Copyright (C) 2004-2008 The Trustees of Indiana University.
- Use, modification and distribution is subject to the Boost Software
- License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt)
-
-===========================
-|Logo| Connected Components
-===========================
-
-::
-
- template<typename Graph, typename ComponentMap>
- inline typename property_traits<ComponentMap>::value_type
- strong_components( const Graph& g, ComponentMap c);
-
- namespace graph {
- template<typename Graph, typename VertexComponentMap>
- void
- fleischer_hendrickson_pinar_strong_components(const Graph& g, VertexComponentMap r);
-
- template<typename Graph, typename ReverseGraph,
- typename ComponentMap, typename IsoMapFR, typename IsoMapRF>
- inline typename property_traits<ComponentMap>::value_type
- fleischer_hendrickson_pinar_strong_components(const Graph& g,
- ComponentMap c,
- const ReverseGraph& gr,
- IsoMapFR fr, IsoMapRF rf);
- }
-
-The ``strong_components()`` function computes the strongly connected
-components of a directed graph. The distributed strong components
-algorithm uses the `sequential strong components`_ algorithm to
-identify components local to a processor. The distributed portion of
-the algorithm is built on the `distributed breadth first search`_
-algorithm and is based on the work of Fleischer, Hendrickson, and
-Pinar [FHP00]_. The interface is a superset of the interface to the
-BGL `sequential strong components`_ algorithm. The number of
-strongly-connected components in the graph is returned to all
-processes.
-
-The distributed strong components algorithm works on both ``directed``
-and ``bidirectional`` graphs. In the bidirectional case, a reverse
-graph adapter is used to produce the required reverse graph. In
-the directed case, a separate graph is constructed in which all the
-edges are reversed.
-
-.. contents::
-
-Where Defined
--------------
-<``boost/graph/distributed/strong_components.hpp``>
-
-also accessible from
-
-<``boost/graph/strong_components.hpp``>
-
-Parameters
-----------
-
-IN: ``const Graph& g``
- The graph type must be a model of `Distributed Graph`_. The graph
- type must also model the `Incidence Graph`_ and be directed.
-
-OUT: ``ComponentMap c``
- The algorithm computes how many strongly connected components are in the
- graph, and assigns each component an integer label. The algorithm
- then records to which component each vertex in the graph belongs by
- recording the component number in the component property map. The
- ``ComponentMap`` type must be a `Distributed Property Map`_. The
- value type must be the ``vertices_size_type`` of the graph. The key
- type must be the graph's vertex descriptor type.
-
-UTIL: ``VertexComponentMap r``
- The algorithm computes a mapping from each vertex to the
- representative of the strong component, stored in this property map.
- The ``VertexComponentMap`` type must be a `Distributed Property Map`_.
- The value and key types must be the vertex descriptor of the graph.
-
-IN: ``const ReverseGraph& gr``
- The reverse (or transpose) graph of ``g``, such that for each
- directed edge *(u, v)* in ``g`` there exists a directed edge
- *(fr(v), fr(u))* in ``gr`` and for each edge *(v', u')* in *gr*
- there exists an edge *(rf(u'), rf(v'))* in ``g``. The functions
- *fr* and *rf* map from vertices in the graph to the reverse graph
- and vice-verse, and are represented as property map arguments. The
- concept requirements on this graph type are equivalent to those on
- the ``Graph`` type, but the types need not be the same.
-
- **Default**: Either a ``reverse_graph`` adaptor over the original
- graph (if the graph type is bidirectional, i.e., models the
- `Bidirectional Graph`_ concept) or a `distributed adjacency list`_
- constructed from the input graph.
-
-IN: ``IsoMapFR fr``
- A property map that maps from vertices in the input graph ``g`` to
- vertices in the reversed graph ``gr``. The type ``IsoMapFR`` must
- model the `Readable Property Map`_ concept and have the graph's
- vertex descriptor as its key type and the reverse graph's vertex
- descriptor as its value type.
-
- **Default**: An identity property map (if the graph type is
- bidirectional) or a distributed ``iterator_property_map`` (if the
- graph type is directed).
-
-IN: ``IsoMapRF rf``
- A property map that maps from vertices in the reversed graph ``gr``
- to vertices in the input graph ``g``. The type ``IsoMapRF`` must
- model the `Readable Property Map`_ concept and have the reverse
- graph's vertex descriptor as its key type and the graph's vertex
- descriptor as its value type.
-
- **Default**: An identity property map (if the graph type is
- bidirectional) or a distributed ``iterator_property_map`` (if the
- graph type is directed).
-
-Complexity
-----------
-
-The local phase of the algorithm is *O(V + E)*. The parallel phase of
-the algorithm requires at most *O(V)* supersteps each containing two
-breadth first searches which are *O(V + E)* each.
-
-
-Algorithm Description
----------------------
-
-Prior to executing the sequential phase of the algorithm, each process
-identifies any completely local strong components which it labels and
-removes from the vertex set considered in the parallel phase of the
-algorithm.
-
-The parallel phase of the distributed strong components algorithm
-consists of series of supersteps. Each superstep starts with one
-or more vertex sets which are guaranteed to completely contain
-any remaining strong components. A `distributed breadth first search`_
-is performed starting from the first vertex in each vertex set.
-All of these breadth first searches are performed in parallel by having
-each processor call ``breadth_first_search()`` with a different starting
-vertex, and if necessary inserting additional vertices into the
-``distributed queue`` used for breadth first search before invoking
-the algorithm. A second `distributed breadth first search`_ is
-performed on the reverse graph in the same fashion. For each initial
-vertex set, the successor set (the vertices reached in the forward
-breadth first search), and the predecessor set (the vertices reached
-in the backward breadth first search) is computed. The intersection
-of the predecessor and successor sets form a strongly connected
-component which is labeled as such. The remaining vertices in the
-initial vertex set are partitioned into three subsets each guaranteed
-to completely contain any remaining strong components. These three sets
-are the vertices in the predecessor set not contained in the identified
-strongly connected component, the vertices in the successor set not
-in the strongly connected component, and the remaing vertices in the
-initial vertex set not in the predecessor or successor sets. Once
-new vertex sets are identified, the algorithm begins a new superstep.
-The algorithm halts when no vertices remain.
-
-To boost performance in sparse graphs when identifying small components,
-when less than a given portion of the initial number of vertices
-remain in active vertex sets, a filtered graph adapter is used
-to limit the graph seen by the breadth first search algorithm to the
-active vertices.
-
-Bibliography
-------------
-
-.. [FHP00] Lisa Fleischer, Bruce Hendrickson, and Ali Pinar. On
- Identifying Strongly Connected Components in Parallel. In Parallel and
- Distributed Processing (IPDPS), volume 1800 of Lecture Notes in
- Computer Science, pages 505--511, 2000. Springer.
-
------------------------------------------------------------------------------
-
-Copyright (C) 2004, 2005 The Trustees of Indiana University.
-
-Authors: Nick Edmonds, Douglas Gregor, and Andrew Lumsdaine
-
-.. |Logo| image:: pbgl-logo.png
- :align: middle
- :alt: Parallel BGL
- :target: http://www.osl.iu.edu/research/pbgl
-
-.. _Sequential strong components: http://www.boost.org/libs/graph/doc/strong_components.html
-.. _Distributed breadth first search: breadth_first_search.html
-.. _Distributed Graph: DistributedGraph.html
-.. _Distributed Property Map: distributed_property_map.html
-.. _Incidence Graph: http://www.boost.org/libs/graph/doc/IncidenceGraph.html
-.. _Bidirectional Graph: http://www.boost.org/libs/graph/doc/BidirectionalGraph.html
-.. _distributed adjacency list: distributed_adjacency_list.html
-.. _Readable Property Map: http://www.boost.org/libs/property_map/ReadablePropertyMap.html
-..
projects / ceph.git / blobdiff