A novel approach to the classical single-row routing problem is presented. The approach is based on a graph-theoretic representation, in which an instance of the single row routing problem is represented by three graphs, a circle graph, a permutation graph, and an interval graph. Three schemes for decomposition of the problem are presented. The decomposition process is applied recursively until either each subproblem is nondecomposable or it belongs to one of the special classes of single row routing problem. For some special classes, it is shown that routing can be done optimally, while solution in other cases can be approximated using heuristic algorithms. These solutions of subproblems are then combined to obtain the solution of the given problem.