Skip Sort — An Adaptive Randomized Algorithm or Expected Time Adaptivity is Best

Abstract

A sorting algorithm is adaptive [15, page 224]_if it requires fewer comparisons to sort a “nearly-sorted” sequence than to sort a “well-shuffled” sequence. Adaptive sorting algorithms are attractive because nearly sorted sequences are common in practice [10,15]. Recently, adaptive sorting has been the subject of intensive investigation [6, 11, 12, 14, 18, 19]. However, the proposed sorting algorithms have received limited acceptance because they are adaptive with respect to only one or two measures [2, 6, 8, 12, 18], they require complex data structures that have a significant overhead [3, 11, 14], or their adaptive behavior has eluded analysis [2, 4, 19]. Moreover, the analysis of the performance of adaptive algorithms has been, so far, based only on worst-case. The notion of optimal adaptivity in the worst case was formalized by Mannila [14]_who quantified disorder with measures of presortedness.KeywordsSorting AlgorithmDistributional ApproachComplex Data StructureCoin TossAdaptive RandomizeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.