Optimal Cache-Aware Suffix Selection

Given string S[1⋯N] and integer k, the suffix selection problem is to determine the kth lexicographically smallest amongst the suffixes S[i ⋯ N], 1 ≤ i ≤ N. We study the suffix selection problem in the cache-aware model that captures two-level memory inherent in computing systems, for a 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 θ (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 = Ω (B1+∈), where ∈ < 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. © G. Franceschini, R. Grossi, and S. Muthukrishnan