Computational topology via functional programming: a baseline analysis

Computational topology is of interest in visualization because it summarizes useful global properties of a dataset. The greatest need for such abstractions is in massive data, and to date most implementations have opted for low-level languages to obtain space and time-efficient implementations. Such code is complex, and is becoming even more so with the need to operate efficiently on a range of parallel hardware. Motivated by rapid advances in functional programming and compiler technology, this chapter investigates whether a shift in programming paradigm could reduce the complexity of the task. Focusing on contour tree generation as a case study, the chapter makes three contributions. First, it sets out the development of a concise functional implementation of the algorithm. Second, it shows that the sequential functional code can be tuned to match the performance of an imperative implementation, albeit at some cost in code clarity. Third, it outlines new possiblilities for parallelisation using functional tools, and notes similarities between functional abstractions and emerging ideas in extreme-scale visualization.