For much of my career, I have been drawn to problems in scientific computing with strong combinatorial undertones. Examples include sparse matrix orderings, load balancing, mesh generation and many others. In any standard taxonomy of scientific computing, these disciplines would be widely scattered, but researchers working in them share a common vocabulary, toolset and aesthetic. By the late nineties, several of us recognized the value of building a community to allow these researchers to interact and to bring visibility to the importance of discrete algorithms in scientific computing. The result was the formation of Combinatorial Scientific Computing community. CSC is concerned with the formulation, application and analysis of discrete methods in scientific applications.
A number of SIAM minisymposia were followed by three successful international workshops and a special issue of ETNA. The next CSC workshop will be held in conjunction with the SIAM Conference on Applied Linear Algebra in 2009. In 2006, DOE funded a SciDAC institute on Combinatorial Scientific Computing and Petascale Simulations, or CSCAPES (pronounced "sea-scapes"). The following paper and talk are an attempt to convey my view of the essence of CSC.
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