In the shortest-paths algorithm we are concerned with the total length of the path between a source (origin) node s and every other node. Suppose instead that we are concerned with the length of the longest edge in a path between the source node and every node. That is, the bottleneck of a path is defined to be the length of the longest edge in the path.

Design an efficient algorithm to solve the single-source smallest bottleneck problem, i.e., find the paths from a source to every other node such that each path has the smallest possible bottleneck. (You may assume that the graph is undirected.)