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Approximation Algorithm for Travelling Salesman Problem

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Názov: Approximation Algorithm for Travelling Salesman Problem
Autori: Oladele, R. O, Mobolaji, D. M.
Zdroj: University of Ibadan Journal of Science and Logics in ICT Research; Vol. 14 No. 1 (2025): Journal of Science and Logics in ICT Research
Informácie o vydavateľovi: University of Ibadan Journal of Science and Logics in ICT Research
Rok vydania: 2025
Zbierka: University of Ibadan Journal System
Predmety: Hamiltonian ath, Linear Programming, Relaxation, Semi-Definite Programming
Popis: Designing approximation algorithms often involves, among other things, relaxing the integrality constraint and obtaining a convex relaxation of the problem. The most well-known relaxation schemes are the Linear Programming (LP) relaxation and Semi-Definite Programing (SDP) relaxation. While LP relaxation has been widely used for solving TSP, SDP has been rarely employed. The primary goal of this paper therefore is to employ SDP and develop approximation algorithm for metric TSP. The SDP relaxation of the TSP is first obtained, and the approximation algorithm is thereafter developed. When compared to optimal results of some standard TSP instances, implementation result showed a relatively fair performance.
Druh dokumentu: article in journal/newspaper
Popis súboru: application/pdf
Jazyk: English
Relation: https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022/1584; https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022
Dostupnosť: https://journals.ui.edu.ng/index.php/uijslictr/article/view/2022
Rights: Copyright (c) 2025 University of Ibadan Journal of Science and Logics in ICT Research
Prístupové číslo: edsbas.5F62B7D0
Databáza: BASE
Popis
Abstrakt:Designing approximation algorithms often involves, among other things, relaxing the integrality constraint and obtaining a convex relaxation of the problem. The most well-known relaxation schemes are the Linear Programming (LP) relaxation and Semi-Definite Programing (SDP) relaxation. While LP relaxation has been widely used for solving TSP, SDP has been rarely employed. The primary goal of this paper therefore is to employ SDP and develop approximation algorithm for metric TSP. The SDP relaxation of the TSP is first obtained, and the approximation algorithm is thereafter developed. When compared to optimal results of some standard TSP instances, implementation result showed a relatively fair performance.