Vicinal Sequencing Problems

This paper describes a special class of sequencing problems called vicinal problems. They are solved by a combination of the methods of graph theory and combinatorial programming. We analyze decomposition possibilities of complete, antisymmetric graphs in order to achieve the partition of the problems into several subproblems that can be solved by combinatorial programming procedures such as back-tracking and branch-and-bound. We conclude by treating a numerical example and commenting on a program written for that purpose.