Rasksort

Rasksort is a sorting algorithm that combines randomized sampling with adaptive partitioning to sort arbitrary sequences efficiently, particularly those with partial order or skewed distributions. The method aims to employ inexpensive distribution estimation from a sample to guide the division of the input into manageable subproblems.

The core idea of rasksort is to proceed in phases. First, a small random sample of elements is drawn to estimate the data distribution. Based on the sample, a set of pivot values is chosen to partition the input into several buckets, each containing elements drawn from a contiguous value range. The partitioning is designed to be stable so that equal keys preserve their relative order. Each bucket is then sorted recursively using rasksort, and the resulting sorted buckets are concatenated to form the final sorted sequence. Some variants use buffer recycling or in-place buffering to reduce extra memory usage.

In terms of performance, the average-case time complexity of rasksort is O(n log n) with high probability, driven by the balanced partitioning of data into buckets. The algorithm uses O(n) extra space for temporary buffers, though in-place variants exist. Stability is achievable when the partitioning preserves the relative order of equal keys. While randomized, the method is designed to avoid pathological inputs in practice; the worst-case bound is typically higher than plain quicksort but remains acceptable in many practical scenarios.

Variants and implementations include rasksort-hybrid (combining a secondary quicksort for small buckets), rasksort-inplace (memory-efficient version), and parallel rasksort for multi-core environments. Rasksort has appeared in theoretical discussions and experimental libraries as a useful approach for sorting large or irregular datasets, though it remains less common in mainstream production code.