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Collective communication operations can dominate the cost of large-scale parallel algorithms. Image compositing in parallel scientific visualization is a reduction operation where this is the case. We present a new algorithm called Radix-k that in many cases performs better than existing compositing algorithms. It does so through a set of configurable parameters, the radices, that determine the number of communication partners in each message round. The algorithm embodies and unifies binary swap and direct-send, two of the best-known compositing methods, and enables numerous other configurations through appropriate choices of radices. While the algorithm is not tied to a particular computing architecture or network topology, the selection of radices allows Radix-k to take advantage of new supercomputer interconnect features such as multiporting. We show scalability across image size and system size, including both powers of two and nonpowers-of-two process counts.
Peterka et al. (Sat,) studied this question.