LCP-Aware Parallel String Sorting

TL;DR

This paper introduces a framework for transforming existing PRAM parallel string sorting algorithms into $D$-aware versions, optimizing work complexity based on the relevant prefix length rather than total input size.

Contribution

It provides a universal method to make any PRAM string sorter $D$-aware, achieving work optimality and minimal time overhead, applicable to deterministic and randomized algorithms.

Findings

Achieves work optimality with respect to the relevant prefix size D

Universal framework applicable to all PRAM string sorters

Minimal logarithmic overhead in execution time

Abstract

When lexicographically sorting strings, it is not always necessary to inspect all symbols. For example, the lexicographical rank of "europar" amongst the strings "eureka", "eurasia", and "excells" only depends on its so called relevant prefix "euro". The distinguishing prefix size $D$ of a set of strings is the number of symbols that actually need to be inspected to establish the lexicographical ordering of all strings. Efficient string sorters should be $D$-aware, i.e. their complexity should depend on $D$ rather than on the total number $N$ of all symbols in all strings. While there are many $D$-aware sorters in the sequential setting, there appear to be no such results in the PRAM model. We propose a framework yielding a $D$-aware modification of any existing PRAM string sorter. The derived algorithms are work-optimal with respect to their original counterpart: If the original algorithm requires $O(w(N))$ work, the derived one requires $O(w(D))$ work. The execution time increases only by a small factor that is logarithmic in the length of the longest relevant prefix. Our framework universally works for deterministic and randomized algorithms in all variations of the PRAM model, such that future improvements in ($D$-unaware) parallel string sorting will directly result in improvements in $D$-aware parallel string sorting.