Combinatorial algorithms such as those that arise in graph analysis, modeling of discrete systems, bioinformatics, and chemistry, are often hard to parallelize. The BLAS library implements key computational primitives for rapid development combinatorial distributed-memory systems. During the decade since its first introduction, has evolved expanded significantly. This article details many techn...

We study the extent to which combinatorial cut conditions determine the maximum network coding rate of k-pairs communication problems. We seek a combinatorial parameter of directed networks which constitutes a valid upper bound on the network coding rate but exceeds this rate by only a small factor in the worst case. (This worst-case ratio is called the gap of the parameter.) We begin by consid...