Computation on large combinatorial structures -- graphs, strings,
partial orders, etc. -- has become fundamental in many areas of data
analysis and scientific modeling. The field of high-performance
combinatorial computing, however, is in its infancy. By way of
contrast, in numerical supercomputing we possess standard algorithmic
primitives, high-performance software libraries, powerful
rapid-prototyping tools, and a deep understanding of effective
mappings of problems to high-performance computer architectures.

This talk will describe several challenges for the field of
combinatorial scientific computing in algorithms, tools,
architectures, and mathematics. I will draw examples from several
applications, and I will highlight our group's work on
high-performance implementation of algebraic primitives for
computation on large graphs.