We study a variant of the Traveling Salesman Problem, where instead of finding a single tour, we want to find a pair of two edge-disjoint tours whose longer tour is as short as possible. We investigate the Price of Diversity (PoD) for this problem, which is the ratio of the cost of the longer of the two tours and the cost of a single optimal tour, in the worst case over all possible instances. We prove (almost) tight bounds on this quantity for a special 1-dimensional scenario and for general metric spaces. We believe that the Price-of-Diversity framework that we introduce is interesting in its own right, and may lead to follow-up work on other problems as well.

翻译：我们研究旅行商问题的一个变体，其目标不再是寻找单一旅行路线，而是寻找一对边不相交的旅行路线，使得其中较长路线的长度尽可能短。我们探讨了该问题的多样性代价，即在所有可能实例的最坏情况下，两条路线中较长路线的成本与单一最优路线成本的比值。我们针对特殊的一维场景和一般度量空间，证明了该量值的（近似）紧确界。我们认为所引入的多样性代价框架本身具有研究价值，并可能推动其他相关问题的后续研究。