Encoding Schemes for Parallel In-Place Algorithms

Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place, that is to use as little auxiliary memory as possible. In this paper, we provide novel in-place algorithms to solve the fundamental problems of merging two sorted sequences, and randomly shuffling a sequence. Both algorithms are work-efficient and have polylogarithmic span. Our algorithms employ encoding techniques which exploit the underlying structure of the input to gain access to more bits, which enables the use of auxiliary data as well as non-in-place methods. The encoding techniques we develop are general. We expect them to be useful in developing in-place algorithms for other problems beyond those already mentioned. To demonstrate this, we outline an additional application to integer sorting. In addition to our theoretical contributions, we implement our merging algorithm, and measure its memory usage and runtime.