.. 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)

===============================================
An Overview of the Parallel Boost Graph Library
===============================================

.. image:: ../graph.png
  :width: 206
  :height: 184
  :alt: An example graph
  :align: right

The Parallel Boost Graph Library (Parallel BGL) is a C++ library for
parallel, distributed computation on graphs. The Parallel BGL contains
distributed graph data structures, distributed graph algorithms,
abstractions over the communication medium (such as MPI), and
supporting data structures. A graph (also called a *network*) consists
of a set of *vertices* and a set of relationships between vertices,
called *edges*. The edges may be *undirected*, meaning that the
relationship between vertices is mutual, e.g., "X is related to Y", or
they can be *directed*, meaning that the relationship goes only one
way, e.g., "X is the child of Y". The following figure illustrates a
typical directed graph, where *a-i* are the vertices and the arrows
represent edges.

.. image:: ../distributed-graph.png
  :width: 229
  :height: 199
  :alt: A distributed graph
  :align: right

The Parallel BGL is primarily concerned with *distributed*
graphs. Distributed graphs are conceptually graphs, but their storage
is spread across multiple processors. The following figure
demonstrates a distributed version of the graph above, where the graph
has been divided among three processors (represented by the grey
rectangles). Edges in the graph may be either local (with both
endpoints stored on the same processor) or remote (the target of the
edge is stored on a different processor).

The Parallel BGL is a generic library. At its core are *generic*
distributed graph algorithms, which can operate on any distributed
graph data structure provided that data structure meets certain
requirements. For instance, the algorithm may need to enumerate the
set of vertices stored on the current processor, enumerate the set of
outgoing edges from a particular vertex, and determine on which
processor the target of each edge resides. The graph algorithms in the
Parallel BGL are also generic with respect to the *properties*
attached to edges and vertices in a graph; for instance, the weight of
each edge can be stored as part of the graph or allocated in a
completely separate data structure. 

The genericity available in the algorithms of the Parallel BGL allows
them to be applied to existing graph data structures. However, most
users will instead be writing new code that takes advantage of the
Parallel BGL. The Parallel BGL provides distributed graph data
structures that meet the requirements of the Parallel BGL
algorithms. The primary data structure is the `distributed adjacency
list`_, which allows storage and manipulation of a (distributed)
graph. The vertices in the graph are divided among the various
processors, and each of the edges outgoing from a vertex are stored on
the processor that "owns" (stores) that vertex. The following figure
illustrates the distributed adjacency list representation.

.. image:: ../dist-adjlist.png
  :width: 446
  :height: 154
  :alt: A distributed adjacency list
  :align: center

.. image:: ../dist-pmap.png
  :width: 271
  :height: 175
  :alt: A distributed property map
  :align: right

The `distributed adjacency list`_ distributes the structure of a graph
over multiple processors. While graph structure is in important part
of many graph problems, there are typically other properties attached
to the vertices and edges, such as edge weights or the position of
vertices within a grid. These properties are stored in *property
maps*, which associate a single piece of data with each edge or vertex
in a graph. Distributed property maps extend this notion to
distributed computing, where properties are stored on the same
processor as the vertex or edge. The following figure illustrates the
distribution of a property map storing colors (white, gray, black) for
each vertex. In addition to the storage for each vertex, the
processors store some "ghost cells" that cache values actually stored
on other processors, represented by the dashed boxes.

Tying together all of the distributed data structures of the Parallel
BGL are its process groups and distributed graph algorithms. Process
groups coordinate the interactions between multiple processes and
distributed data structures by abstracting the communication
mechanism. The algorithms are typically written using the SPMD model
(Single Program, Multiple Data) and interact with both the distributed
data structures and the process group itself. At various points in the
algorithm's execution, all processes execute a synchronization point,
which allows all of the distributed data structures to ensure an
appropriate degree of consistency across processes. The following
diagram illustrates the communication patterns within the the
execution of a distributed algorithm in the Parallel BGL. In
particular, the diagram illustrates the distributed data structures
used in a distributed breadth-first search, from the top-left and
proceeding clockwise:

   - a user-defined property map that tracks the distance from the
     source vertex to all other vertices,

   - an automatically-generated property map that tracks the "color"
     of vertices in the (distributed) graph, to determine which
     vertices have been seen before,

   - a distributed queue, which coordinates the breadth-first search
     and distributes new vertices to search, and

   - a distributed graph, on which the breadth-first search is
     operating.

.. image:: ../architecture.png
  :width: 485
  :height: 410
  :alt: Parallel Boost Graph Library architecture
  :align: center

----------------------------------------------------------------------------

Copyright (C) 2005 The Trustees of Indiana University.

Authors: Douglas Gregor and Andrew Lumsdaine

.. _Distributed adjacency list: distributed_adjacency_list.html
.. _Process groups: