A company named RT&T has a network of n switching stations connected by m high-speed communication links. Each customer’s phone is directly connected to one station in his or her area. The engineers...

A company named RT&T has a network of
n
switching stations connected

by
m
high-speed communication links. Each customer’s phone is directly

connected to one station in his or her area. The engineers of RT&T have

developed a prototype video-phone system that allows two customers to

see each other during a phone call. In order to have acceptable image

quality, however, the number of links used to transmit video signals between

the two parties cannot exceed 4. Suppose that RT&T’s network is

represented by a graph. Design an efficient algorithm that computes, for

each station, the set of stations it can reach using no more than 4 links.