(Path Bottleneck Problem) Consider the framework of the shortest path problem. For any path P, define the bottleneck arc of P as an arc that has maximum length over all arcs of P. Consider the problem of finding a path connecting two given nodes and having minimum length of bottleneck arc. Derive an analog of Prop. 2.1 for this problem. Consider also a single origin/all destinations version of this problem. Develop an analog of the generic algorithm of Section 2.2 and prove an analog of Prop. 2.2.