Optimal cache-aware suffix selection

TL;DR

This paper introduces an optimal cache-aware algorithm for the suffix selection problem that minimizes block transfers in two-level memory systems, outperforming traditional permutation bounds.

Contribution

It presents the first optimal cache-aware suffix selection algorithm with $ ilde{O}(N/B)$ block transfers for unbounded alphabets under the tall-cache assumption.

Findings

Achieves optimal $ ilde{O}(N/B)$ block transfers.

Works for strings over unbounded alphabets.

Surpasses the permutation bottleneck bound.

Abstract

Given string $S[1..N]$ and integer $k$, the {\em suffix selection} problem is to determine the $k$th lexicographically smallest amongst the suffixes $S[i... N]$, $1 \leq i \leq N$. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a \emph{cache} of limited size $M$ and block size $B$. The complexity of interest is the number of block transfers. We present an optimal suffix selection algorithm in the cache-aware model, requiring $\Thetah{N/B}$ block transfers, for any string $S$ over an unbounded alphabet (where characters can only be compared), under the common tall-cache assumption (i.e. $M=\Omegah{B^{1+\epsilon}}$, where $\epsilon<1$). Our algorithm beats the bottleneck bound for permuting an input array to the desired output array, which holds for nearly any nontrivial problem in hierarchical memory models.