From: Wolfgang Bangerth Date: Wed, 6 Nov 2013 17:17:35 +0000 (+0000) Subject: Add more information to the graph coloring function. X-Git-Tag: v8.1.0~374 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=82a6411229b6fc923fbb3abf60ce3b94020bb687;p=dealii.git Add more information to the graph coloring function. git-svn-id: https://svn.dealii.org/trunk@31566 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/news/changes.h b/deal.II/doc/news/changes.h index b4eab15de5..b9500bc0c2 100644 --- a/deal.II/doc/news/changes.h +++ b/deal.II/doc/news/changes.h @@ -203,6 +203,12 @@ inconvenience this causes.

Specific improvements

    +
  1. New: There is now a framework for coloring graphs, with functions + in namespace GraphColoring. +
    + (Bruno Turcksin, Martin Kronbichler, 2013/11/06) +
    2. +
  2. Fixed: the DerivativeApproximation class was not working correctly when used with parallel vectors. diff --git a/deal.II/include/deal.II/base/graph_coloring.h b/deal.II/include/deal.II/base/graph_coloring.h index 64f39e54ae..b38d1a5717 100644 --- a/deal.II/include/deal.II/base/graph_coloring.h +++ b/deal.II/include/deal.II/base/graph_coloring.h @@ -32,27 +32,89 @@ DEAL_II_NAMESPACE_OPEN /// This namespace contains the functions necessary to color a graph. -namespace graph_coloring { - +namespace graph_coloring +{ /** - * Create the partitioning using a simplified version of the Cuthill-McKee - * algorithm (Breadth First Search algorithm). + * Create a partitioning of the given range of iterators using a simplified + * version of the Cuthill-McKee algorithm (Breadth First Search algorithm). + * Any pair of two iterators that point to conflicting objects will be placed + * into different partitions, where the question whether two objects conflict + * is determined by a user-provided function. + * + * This function can also be considered as a graph coloring: each object + * pointed to by an iterator is considered to be a node and there is an + * edge between each two nodes that conflict. The graph coloring algorithm + * then assigns a color to each node in such a way that two nodes connected + * by an edge do not have the same color. + * + * A typical use case for this function is in assembling a matrix in parallel. + * There, one would like to assemble local contributions on different cells + * at the same time (an operation that is purely local and so requires + * no synchronization) but then we need to add these local contributions + * to the global matrix. In general, the contributions from different cells + * may be to the same matrix entries if the cells share degrees of freedom + * and, consequently, can not happen at the same time unless we want to + * risk a race condition (see http://en.wikipedia.org/wiki/Race_condition ). + * Thus, we call these two cells in conflict, and we can only allow operations + * in parallel from cells that do not conflict. In other words, two cells + * are in conflict if the set of matrix entries (for example characterized + * by the rows) have a nonempty intersection. + * + * In this generality, computing the graph of conflicts would require calling + * a function that determines whether two iterators (or the two objects they + * represent) conflict, and calling it for every pair of iterators, i.e., + * $\frac 12 N (N-1)$ times. This is too expensive in general. A better + * approach is to require a user-defined function that returns for every + * iterator it is called for a set of indicators of some kind that characterize + * a conflict; two iterators are in conflict if their conflict indicator sets + * have a nonempty intersection. In the example of assembling a matrix, + * the conflict indicator set would contain the indices of all degrees of + * freedom on the cell pointed to (in the case of continuous Galerkin methods) + * or the union of indices of degree of freedom on the current cell and all + * cells adjacent to the faces of the current cell (in the case of + * discontinuous Galerkin methods, because there one computes face integrals + * coupling the degrees of freedom connected by a common face -- see step-12). + * However, in other situations, these conflict indicator sets may represent + * something different altogether -- it is up to the caller of this function + * to describe what it means for two iterators to conflict. Given this, + * computing conflict graph edges can be done significantly more cheaply + * than with ${\cal O}(N^2)$ operations. + * + * In any case, the result of the function will be so that iterators whose + * conflict indicator sets have overlap will not be assigned to the same + * partition (i.e., they will have a different color). + * + * @param[in] begin The first element of a range of iterators for which a + * partitioning is sought. + * @param[in] end The element past the end of the range of iterators. + * @param[in] get_conflict_indices A user defined function object returning + * a set of indicators that are descriptive of what represents a + * conflict. See above for a more thorough discussion. + * @return A set of sets of iterators (where sets are represented by + * std::vector for efficiency). Each element of the outermost set + * corresponds to the iterators pointing to objects that are in the + * same partition (have the same color) and consequently do not + * conflict. The elements of different sets may conflict. + * + * @author Martin Kronbichler, Bruno Turcksin */ template - std::vector > create_partitioning(Iterator const &begin, - typename identity::type const &end, - std_cxx1x::function (Iterator const &)> - const &get_conflict_indices) + std::vector > + create_partitioning(const Iterator &begin, + const typename identity::type &end, + const std_cxx1x::function (Iterator const &)> &get_conflict_indices) { std::vector > partitioning(1,std::vector (1,begin)); + // Number of iterators. - unsigned int n_iterators(0); + unsigned int n_iterators = 0; + // Create a map from conflict indices to iterators boost::unordered_map > indices_to_iterators; for (Iterator it=begin; it!=end; ++it) { std::vector conflict_indices = get_conflict_indices(it); - const unsigned int n_conflict_indices(conflict_indices.size()); + const unsigned int n_conflict_indices = conflict_indices.size(); for (unsigned int i=0; i