1. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. When Don’t I Use MPI? Jonathan Berry Scalable Algorithms Department Sandia National Laboratories June 3, 2008

2. Informatics Datasets Are Different Informatics: The analysis of datasets arising from “information” sources such as the WWW (not physical simulation) Motivating Applications: Homeland security Computer security (DOE emphasis) Biological networks, etc. Primary HPC Implication: Any partitioning is “bad” “One of the interesting ramifications of the fact that the PageRank calculation converges rapidly is that the web is an expander-like graph” Page, Brin, Motwani,Winograd 1999 From UCSD ‘08 Broder, et al. ‘00

3. Informatics Usage Models Can Be Quite Different Joe: 4 proc. Sally: 4 proc.Sue: 4 proc. memory ref. Shared, Hashed Data

4. PageRank performs a sequence of matrix- vector multiplications “NICE” data are “R-MAT” graphs with maximum degree ~1000 “NASTY” data are R-MAT graphs with maximum degree ~200k The MTA-2 runs are nearly data agnostic and have ideal speedup through 20p The end of MTA-2 scaling indicates that algorithmic work is needed (we’ve seen and overcome behavior like this before) Multithreaded Architectures Can Boost Performance [K. Devine, S. Plimpton, Berry] 33M vertices, 268M directed edges Number of Processors PageRank time

5. MTA/XMT Programming: Use the Compiler Here, we sum a quantity over the neighbors of one vertex The removal of the reduction of “sum” prevents a hot spot This output is from “canal,” an MTA/XMT compiler analysis tool

6. We Are Developing The MultiThreaded Graph Library Enables multithreaded graph algorithms (XMT, SMP, Niagara) Builds upon community standard (Boost Graph Library) Abstracts data structures and other application specifics Hide some shared memory issues Preserves good multithreaded performance MTGL ADAPTER MTGL C C S-T connectivity scaling (MTA-2)SSSP scaling (MTA-2) MTA-2 Processors Solve time (sec)

7. Current MTGL Algorithms Connected components (psearch, visit_edges, visit_adj) Strongly-connected components (psearch) Maximal independent set (visit_edges) Typed subgraph isomorphism (psearch, visit_edges) S-t connectivity (bfs) Single-source shortest paths (psearch) Betweenness centrality (bfs-like) Community detection (all kernels) Connection subgraphs (bfs, sparse matrix, mt-quicksort) Find triangles (psearch) Find assortativity (psearch) Find modularity (psearch) PageRank (matvec) Network Simplex for MaxFlow Under development: Motif detection more Berkeley Open-Source Licence pending

8. Acknowledgements MultiThreading Background Simon Kahan (formerly Cray) Petr Konecny (Google (formerly Cray)) MultiThreading/Distributed Memory Comparisons Karen Devine (Sandia) Steve Plimpton (Sandia) MTGL Algorithm Design and Development Vitus Leung (Sandia) Kamesh Madduri (Georgia Tech.) William McLendon (Sandia) Cynthia Phillips (Sandia) Generic Programming Background Andrew Lumsdaine (Indiana U.) Doug Gregor (Indiana U.)