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.

Authors: Brian Barrett, Douglas Gregor, and Andrew Lumsdaine