Background: During the COVID-19 pandemic, online learning has played an increasingly crucial role in the educational system. Academic dishonesty (AD) in online learning is a challenging problem that represents a complex psychological and social phenomenon for learners. However, there is a lack of comprehensive and systematic reviews of AD in online learning environments.Objectives: This study presents a systematic study of AD in online learning environments to delineate its trends and uncover potential areas for further research.Methods: We conducted this review based on various sources of evidence-based research and followed the guidelines of the PRISMA statement and procedure for selection. After the exclusion criteria were employed, 59 eligible articles were selected and then analysed in a descriptive overview. Two frameworks were identified in the structured content analysis to analyse these articles. One was the framework of Gilbert's Behaviour Engineering Model (BEM), and the other was the types of interventions for online AD, where 36 articles were analysed. Results and Conclusions:The descriptive results showed that most studies used quantitative methods and focused on students. The analysis results of influencing factors under the BEM framework showed that the category of environment support and tools accounts for the largest proportion.

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In this article, we present a new data structure, called the permutation tree, to improve the running time of sorting permutation by transpositions and sorting permutation by block interchanges. The existing 1.5-approximation algorithm for sorting permutation by transpositions has time complexity O ( n 3/2 √ logn ). By means of the permutation tree, we can improve this algorithm to achieve time complexity O ( nlogn ). We can also improve the algorithm for sorting permutation by block interchanges to take its time complexity from O ( n 2 ) down to O ( nlogn ).