Assume we have an graph $\backslash ($ G $\backslash )$ with $\backslash ($ n $\backslash )$ vertices and m edges. We have two balls $\backslash ($ B$\_\{1\},$ B$\_\{2\}\backslash )$ that will move along their designed path $\backslash ($ P$\_\{1\},$ P$\_\{2\}\backslash ).$ Both balls will start at $\backslash ($ P$\_\{1\}[1]\backslash )$ and $\backslash ($ P$\_\{2\}[1]\backslash ),$ and can move only forward along their designed paths. To be more precise, we define a valid move for a ball is either stay in it's current node, or move to the next node on its path. Each ball makes exactly one legal move in each round. A sequence, specifying in each round a valid move for each robot, is a plan.

The score of a plan is the maximum distance of the two balls from each other at any moment during the execution of the plan.

Describe an algorithm that computes the minimum score plan for the two balls. Your algorithm should be as fast as possible.