{"title":"Shell sort with expected complexity of O(nlog2n)","authors":"Shengrong Hu","doi":"10.1016/j.tcs.2025.115122","DOIUrl":null,"url":null,"abstract":"<div><div>Theoretical analysis of the Shell sort algorithm has been a longstanding challenge, and there have been no reports of a Shell sort algorithm with a complexity of O(<em>n</em>log<sub>2</sub><em>n</em>). This study investigated the efficiency of the Shell sort algorithm using a specific increment sequence and conducted stability fitting. The fitting results strongly suggest that the number of key comparisons and movements follows the form c<em>n</em>ln(<em>n</em>)+d<em>n</em><sup>λ</sup>ln(<em>n</em>), where λ<1, implying an overall complexity of O(<em>n</em>log<sub>2</sub><em>n</em>).</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1034 ","pages":"Article 115122"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S030439752500060X","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Theoretical analysis of the Shell sort algorithm has been a longstanding challenge, and there have been no reports of a Shell sort algorithm with a complexity of O(nlog2n). This study investigated the efficiency of the Shell sort algorithm using a specific increment sequence and conducted stability fitting. The fitting results strongly suggest that the number of key comparisons and movements follows the form cnln(n)+dnλln(n), where λ<1, implying an overall complexity of O(nlog2n).
期刊介绍：
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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