Discrete Tomography Problems with Paired Projections and Complexity Characteristics

This paper presents a study of discrete tomography problems with horizontal, vertical, and paired projections, where paired projections reflect the conditions of generalized degree sequences of hypergraphs. Paired projections, as far as we know, are considered for the first time in the problems of discrete tomography. The general purpose of introducing these projections is to involve more information about the object under consideration in order to narrow the class of all possible solutions when a solution exists. On the other hand, the consideration of pairwise projections successfully complements our previous research, which is devoted to the study of structures with different classes. In this paper, we consider different types of pairwise projections, including the set of all pairs of columns, the set of all pairs with one fixed column, and the set of all pairs of neighboring columns; and investigate the complexity characteristics of the corresponding problems.