On The Average-Case Complexity of Shellsort
Paul M.B. Vitanyi (National Research Center for Mathematics and, Computer Science in the Netherlands (CWI), Univrsity of Amsterdam)
TL;DR
This paper establishes a precise lower bound on the average-case complexity of Shellsort based on increment sequences, confirming its sharpness and deriving new exact results for specific cases like the 3-pass scenario.
Contribution
It introduces a sharp lower bound on Shellsort's average-case complexity tied to increment sequences and provides exact results for particular cases such as the 3-pass version.
Findings
Lower bound on average-case complexity based on increment sequences
The bound is sharp in all verifiable cases
Exact complexity results for the 3-pass Shellsort case
Abstract
We prove a lower bound expressed in the increment sequence on the average-case complexity of the number of inversions of Shellsort. This lower bound is sharp in every case where it could be checked. A special case of this lower bound yields the general Jiang-Li-Vit\'anyi lower bound. We obtain new results e.g. determining the average-case complexity precisely in the Yao-Janson-Knuth 3-pass case.
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Taxonomy
TopicsCellular Automata and Applications · Computability, Logic, AI Algorithms · Algorithms and Data Compression