Optimal Cache-Aware Suffix Selection

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 $S[ildots N]$, $1 leq i leq N$. 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 $Thetaleft(N/Bright)$ block transfers, for any string $S$ over an unbounded alphabet (where characters can only be compared), under the common tall-cache assumption (i.e. $M=Omegaleft(B^{1+epsilon}right)$, 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