In a synchronous optical network (SONET) ring, a collection of routers are connected with fiber-optic cables to form a single, simple cycle. A message between two routers, x and y, can then be transmitted by routing it clockwise or counter-clockwise around the ring. Given a set, M, of messages to transmit, each specified by a pair of routers (x, y), the ring-loading problem is to route all the messages in M so as to minimize the maximum load on any link in the ring (that joins two adjacent routers). Solving such an optimization problem is useful, since such a solution minimizes the bandwidth needed to transmit all the messages in M. Describe a 2-approximation for solving the ring-loading problem.