# Connected Components Parallel Search

    namespace graph { namespace distributed {
      template<typename Graph, typename ComponentMap>
      typename property_traits<ComponentMap>::value_type
      connected_components_ps(const Graph& g, ComponentMap c)
    } }

The `connected_components_ps()` function computes the connected components of a graph by performing a breadth-first search from several sources in parallel while recording and eventually resolving the collisions.

Contents

- Where Defined
- Parameters
- Complexity
- Algorithm Description

# Where Defined

<`boost/graph/distributed/connected_components_parallel_search.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 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.

# Complexity

O(PN^2 + VNP) work, in O(N + V) time, where N is the number of mappings and V is the number of local vertices.

# Algorithm Description

Every N th nodes starts a parallel search from the first vertex in their local vertex list during the first superstep (the other nodes remain idle during the first superstep to reduce the number of conflicts in numbering the components). At each superstep, all new component mappings from remote nodes are handled. If there is no work from remote updates, a new vertex is removed from the local list and added to the work queue.

Components are allocated from the `component_value_allocator` object, which ensures that a given component number is unique in the system, currently by using the rank and number of processes to stride allocations.

When two components are discovered to actually be the same component, a collision is recorded. The lower component number is prefered in the resolution, so component numbering resolution is consistent. After the search has exhausted all vertices in the graph, the mapping is shared with all processes and they independently resolve the comonent mapping. This phase can likely be significantly sped up if a clever algorithm for the reduction can be found.

Copyright (C) 2009 The Trustees of Indiana University.

Authors: Brian Barrett, Douglas Gregor, and Andrew Lumsdaine