{"title":"Updated Estimates for Algorithms for Packing\u00002-Bar Charts in a Strip","authors":"S. A. Nazarenko","doi":"10.1134/S1990478924040112","DOIUrl":"10.1134/S1990478924040112","url":null,"abstract":"<p> We consider a two-bar charts packing problem in which it is necessary to pack bar charts\u0000consisting of two bars in a unit-height strip of minimum length. Each bar has a height of at most\u00001 and unit length. The problem under consideration is NP-hard and generalizes the bin packing\u0000problem and two-dimensional vector packing problem. This paper proves updated accuracy\u0000estimates and time complexity for several previously developed polynomial approximation\u0000algorithms for the two-bar charts packing problem and particular cases of the problem. We show\u0000the attainability of the estimates. Furthermore, we consider a problem of packing an unlimited\u0000number of bar charts belonging to\u0000<span>( k )</span> different types and propose a polynomial algorithm to solve the problem in\u0000case\u0000<span>( k = text {const} )</span>.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 4","pages":"759 - 774"},"PeriodicalIF":0.58,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}