Fast Algorithm to Find 2-Factor of Minimum Weight.

The paper considers the minimization of the sum of weights of edges forming a subset U′ ⊂ U of the set of disjoint simple cycles at vertices υ ϵ V in graph H = (V,U) and covering V. The problem under study (2-f problem) is polynomially solvable in algorithms that are characterized by technical difficulties that hinder the acceleration of computing. The 2-f problem is solved by reducing it to a simpler bipartite case. The result is represented by a perfect matching of bipartite graph corresponding to the solution of the assignment problem, where each circuit of cyclic expansion contains at least three arcs. [ABSTRACT FROM AUTHOR]