We present a time-efficient algorithm to find an exact solution for the single-row routing problem in this paper. The proposed algorithm is based on the branch-and-bound technique and the interval graphical representation model in [3]. In each stage of the algorithm, an upper bound is obtained by creating a heuristic routing while a lower bound is obtained from the cut numbers in an incomplete graphical interval representation. These bounding values will be computed rapidly by proposed methods. To reduce computing time, we adopt an "outer-track-first" branching strategy and a data tree structure. An ε-optimal routing can be obtained if the preset CPU time is exhausted. Computational experience is cited for some generated test problems of up to 50 nets and 150 nodes.