Combinatorial algorithms have long played a crucial, albeit under-recognized role enabling scientific computations. This is particularly true of the tera- and peta-scale simulations at the heart of SciDAC. Graph and geometric algorithms are crucial tools for load balancing parallel computations; graphs are an essential component of automatic differentiation techniques in large scale optimization; graphs are central to solving many problems in sparse linear algebra; etc. This poster will review recent developments in this important area, highlighting impact on SciDAC applications.