In this paper, we give a simple polynomial-time reduction of {L(p)-Labeling} on graphs with a small diameter to {Metric (Path) TSP}, which enables us to use numerous results on {(Metric) TSP}. On the practical side, we can utilize various high-performance heuristics for TSP, such as Concordo and LKH, to solve our problem. On the theoretical side, we can see that the problem for any p under this framework is 1.5-approximable, and it can be solved by the Held-Karp algorithm in O(2^n n^2) time, where n is the number of vertices, and so on.

翻译：本文给出了一种从具有小直径图上的{L(p)-标号}问题到{度量(路径)TSP}问题的简单多项式时间归约，这使得我们能够利用{(度量)TSP}问题的丰富研究成果。在实际应用层面，我们可以借助TSP的各种高性能启发式算法（如Concorde和LKH）来求解该问题。在理论层面，我们证明在此框架下任意p值对应的问题可实现1.5-近似，并且可以通过Held-Karp算法在O(2^n n^2)时间内求解（其中n为顶点数）。