Optimal solutions of combinatorial optimization problems can be sensitive to changes in the cost of one or more elements of the ground set E. Single and set tolerances measure the supremum / infimum possible change such that the current solution remains optimal for cost changes in one or more elements. The current definition does not apply to all elements of E or to all subsets of E. In this work, we broaden the definition to all elements for single tolerances and to all subsets of elements for set tolerances, while proving that key theoretical and computational properties still apply.

翻译：组合优化问题的最优解可能对基础集E中一个或多个元素成本的变动敏感。单元素容差与集合容差分别度量当单个或多个元素成本变动时，当前解保持最优性所允许的成本变动上确界/下确界。现有定义无法适用于E的所有元素或E的所有子集。本工作中，我们将单元素容差定义扩展至所有元素，将集合容差定义扩展至所有元素子集，并证明关键的理论与计算性质在此扩展后依然成立。