Repeated Recursion Unfolding for Super-Linear Speedup within Bounds

TL;DR

This paper introduces repeated recursion unfolding, a technique that can significantly reduce recursive computation time by transforming recursion into a form that allows super-linear speedup within specified bounds.

Contribution

It presents a novel recursion unfolding method that achieves super-linear speedup and reduces time complexity, supported by theoretical proofs and initial prototype results.

Findings

Super-linear speedup theorem proven for best case scenarios.

Runtime improvements reach several orders of magnitude.

Recursion can be completely removed up to a chosen bound.

Abstract

Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of unfolded rules to the program. Efficiency crucially depends on the amount of simplification inside the unfolded rules. We prove a super-linear speedup theorem in the best case, i.e. speedup by more than a constant factor. Our optimization can lower the time complexity class of a program. In this paper, the super-linear speedup is within bounds: it holds up to an arbitrary but chosen upper bound on the number of recursive steps. We also report on the first results with a prototype implementation of repeated recursion unfolding. A simple program transformation completely removes recursion up to the chosen bound. The actual runtime improvement quickly reaches several orders of magnitude.