Graph algorithms tend to suffer poor performance due to the irregularity of access patterns within general graph data structures, arising from poor data locality, which translates to high memory latency. The result is that advances in high-performance solutions for graph algorithms are most likely to come through advances in both architectures and algorithms. Specialized MMT shared memory machines offer a potentially transformative environment in which to approach the problem. Here, we explore the challenges of implementing Subgraph Isomorphism (SI) algorithms based on the Ullmann and VF2 algorithms in the Cray XMT environment, where issues of memory contention, scheduling, and compiler parallelizability must be optimized. Copyright is held by the author/owner(s).
We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.