Vertex Reordering Algorithms for Cluster Identification

Vertex Ordering, Clustering, and Their Application to Graph Partitioning

We propose a new heuristic for vertex ordering and a method that splits the vertex ordering into clusters. We apply them to the graph partitioning problem. The application of these ideas incorporates reordering in genetic algorithms and the identification of clustered structures in graphs. Experimental tests on benchmark graphs showed that the new vertex-ordering scheme performed better than ex...

Sparse Matrix Reordering Algorithms for Cluster Identification

Exact and Heuristic Minimization of Determinant Decision Diagrams

Determinant Decision Diagram (DDD) is a variant of binary decision diagrams (BDDs) for representing symbolic matrix determinants and cofactors in symbolic circuit analysis. DDD-based symbolic analysis algorithms have time and space complexities proportional to the number of DDD vertices. Inspired by the ideas of Rudell, Drechsler, et. al. on BDD minimization, we present lowerbound based exact a...

Vertex-ordering Algorithms for Automatic Differentiation of Computer Codes

In the context of Automatic Differentiation of functions represented by computer code via the vertex elimination approach first advocated by Griewank and Reese (Automatic Differentiation of Algorithms, SIAM, 1991, p126-135), we present two approximate algorithms based on the linearised computational graph of the input code. The first is a statement reordering algorithm aiming to tune the AD-gen...

Adjacency-based data reordering algorithm for acceleration of finite element computations

Effective use of the processor memory hierarchy is an important issue in high performance computing. In this work, a part level mesh topological traversal algorithm is used to define a reordering of both mesh vertices and regions that increases the spatial locality of data and improves overall cache utilization during on processor finite element calculations. Examples based on adaptively create...