A number of practical tasks require minimizing the human and material resources that are involved in tasks or time expenditures. A special place in this class of problems is occupied by theoretical problems that have a broad practical application, which belong to a class of discrete optimization problems. When minimizing time expenditures in such problems the question of determining the optimal sequencing of execution of a finite set of works (tasks, operations, projects, etc.) is raised. This sequencing can be linear, circular or parallel. The latter is considered by the authors. This article is devoted to the analysis of one of the problems of discrete optimization, which belongs to the class of problems of the scheduling theory, and, taking into account its specificity, can be considered as an optimization graph problem. Specifically, in terms of the theory of graphs, the problem of finding a parallel sequencing of vertices of a given graph of minimum length, in which at each place there is no more than a given fixed number of vertices, is under consideration. Since this problem is NP-hard, its exact solution can be found by using one of the methods that implements state search scheme. The authors investigated the impact of the accuracy of the estimation of the length of optimal sequencing on the rate of finding the solution by using one of the most common methods, namely the branch and bound method. As a result, an improved lower-bound estimate of time expenditures was obtained and an upper-bound estimate was proposed. The latter was used to justify the relationship of the problem under consideration with the inverse one. Also, on the basis of the computational experiment results were obtained that refuted the a priori consideration about the impact of the accuracy of the estimation on the rate of finding the exact solution by using the branch and bound method
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