Fast Algorithm to Find 2-Factor of Minimum Weight

Constructing an algorithm of quadratic time complexity for finding the maximal matching

“…Study [3] proposes the use of relaxations as the elements of algorithms and methods for solving the problems on building closed routes, including within the methods of branches and boundaries. Work [4] proposes to use the 2-factor of the minimum weight as a relaxation to the salesman problem within the branch and boundary method. Article [5] reports analysis of the approximate algorithm for solving the metric problem of a salesman with an accuracy estimate of 1.5, using the algorithm for obtaining the perfect matching combination.…”

“…The above works [1][2][3][4][5] suggest solving auxiliary subproblems in order to speed up calculations in accurate, and improve accuracy in approximate, methods for solving the problems on building closed routes, at the steps of the relevant algorithms. At the same time, the cited studies do not address issues related to better implementations or lower computational complexity of existing algorithms, which could speed up the construction of closed routes.…”

“…One of the problems that can be used as a relaxation to an NP-complete salesman problem [3,4] is the problem about matching (MP). In [4], a solution to MP is used as an element of the algorithm to obtain an approximate solution to the salesman's problem.…”

“…One of the problems that can be used as a relaxation to an NP-complete salesman problem [3,4] is the problem about matching (MP). In [4], a solution to MP is used as an element of the algorithm to obtain an approximate solution to the salesman's problem. The downside of the algorithm from [4] is its computational complexity, specifically O(n 4 ), which makes the algorithm almost unusable for real-time use.…”

“…In [4], a solution to MP is used as an element of the algorithm to obtain an approximate solution to the salesman's problem. The downside of the algorithm from [4] is its computational complexity, specifically O(n 4 ), which makes the algorithm almost unusable for real-time use. The relevant area of research is to derive a faster algorithm for solving MP, which would speed up the implementation of algorithm [4].…”