Finding the Optimal Paths in a Boolean-Valued Network

Finding multiple alternative shortest paths between two nodes in a network is an important problem of computer science. In this paper, we consider a special case of this problem, when the costs of all arcs are some elements of a fixed finite Boolean algebra. We propose two different exact algorithms for finding a given number of optimal paths in a Boolean-valued network. To clarify the proposed algorithms, two examples were considered in the final part of the paper.