Formal Programming for the Shortest Path and Its Critical Edge Problems

Many problems in operations research can be formulated in terms of networks, among which the shortest path is a particularly important class. Using the PAR method, we formally derive and implement algorithmic programs for three typical network problems, including the shortest path tree (SPT) problem, the most vital edge (MVE) problem, and the real time critical edge (RTCE) problem, which are motivated by routing applications. The main ideas and ingenuity of these algorithms are revealed by formula deduction.