Applying permutations to optimize topological sorting algorithms in discrete mathematical structures

Abhyankar, Girish; Sharma, Chetan Kumar; Malagi, Veeresh; Chaudhari, Archana; Rao, N. Eswara; Rao, M. Purnachandra

doi:10.47974/JDMSC-2474

Open Access Research Article

Applying permutations to optimize topological sorting algorithms in discrete mathematical structures

Girish Abhyankargabhyankar@symlaw.ac.inSymbiosis Law SchoolSymbiosis Centre for Advanced Legal Studies and Research (SCALSAR), Symbiosis International (Deemed University)Pune, Maharashtra, 411014, IndiaView full profile → , Chetan Kumar Sharmachetan.sharma@niu.edu.inDepartment of School of SciencesNoida International UniversityNoida, Uttar Pradesh, 203201, IndiaView full profile → , Veeresh Malagism.veeresh@jainuniversity.ac.inDepartment of MathematicsFaculty of Engineering and TechnologyJAIN (Deemed-to-be University)Bengaluru, Karnataka, 560069, IndiaView full profile → , ^*Archana ChaudhariCorresponding authorarchana.chaudhari@vit.eduDepartment of Instrumentation EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , N. Eswara Raoeswararao@gmail.comDepartment of Master of Computer ApplicationsKITS Akshar Institute of TechnologyGuntur, Andhra Pradesh, 522019, IndiaView full profile → , M. Purnachandra Raopurnachandrarao@gmail.comDepartment of Information TechnologyKKR and KSR Institute of Technology and SciencesGuntur, Andhra Pradesh, 522017, IndiaView full profile →

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pp. 429–436Vol. 29Issue 2-AFebruary 2026DOI: 10.47974/JDMSC-2474 Crossmark XML

Received:: 07 May 2025
Published Online:: 31 Dec 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2474
Pages:: 429–436

Abstract

In discrete mathematics, topological sorting is very important, especially when working with directed acyclic graphs (DAGs). Optimizing topological sorting methods is important for making computers work faster in many situations, such as when planning tasks, figuring out dependencies, and designing circuits. This paper looks at how permutations can be used to make topological sorting better by using their structure features to make computations simpler. We proposed a new technique that improves contemporary topological sorting algorithms via the use of permutation-based totally upgrades. The advised way seems for traits in the structure of the layout and uses permutation groups to arrange the nodes, slicing down on processing steps that aren’t wished. The suggested method is an awful lot quicker than well-known algorithms, especially while running with huge graphs, as shown via both theoretical evaluation and testing consequences. This study gives us a fresh look at topological sorting and helps us figure out how to make algorithms work better in real-life situations where time and computer power are limited.

Keywords

Topological sorting Permutations Directed acyclic graphs (DAGs)Algorithm optimization Computational complexity

Subject Classifications

68Rxx

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