High-performance combinatorial algorithms

Combinatorial algorithms have long played an important role in many applications of scientific computing such as sparse matrix computations and parallel computing. The growing importance of combinatorial algorithms in emerging applications like computational biology and scientific data mining calls for development of a high performance library for combinatorial algorithms. Building such a library requires a new structure for combinatorial algorithms research that enables fast implementation of new algorithms. We propose a structure for combinatorial algorithms research that mimics the research structure of numerical algorithms. Numerical algorithms research is nicely complemented with high performance libraries, and this can be attributed to the fact that there are only a small number of fundamental problems that underlie numerical solvers. Furthermore there are only a handful of kernels that enable implementation of algorithms for these fundamental problems. Building a similar structure for combinatorial algorithms will enable efficient implementations for existing algorithms and fast implementation of new algorithms. Our results will promote utilization of combinatorial techniques and will impact research in many scientific computing applications, some of which are listed