— We address the problem of connection preemption in a multi-class network environment. Our objective is: i) to minimize the number of preempted connections, and ii) to minimize the total preempted bandwidth, in that order. We show that this problem is NP-complete by reducing it to a well-known NP complete problem – the subset sum problem. Therefore, any polynomial time algorithm, such as Minn Conn [1], to solve this problem is suboptimal. We present an optimal algorithm with exponential complexity that can be used when the network load is light. We also present a fully polynomial time approximation algorithm that performs within a bounded factor from the optimal, and can be used in large networks having thousands of connections. We compare the performance of exact and approximate algorithms in a practical scenario by conducting simulations on a network representing twenty largest metros in the U.S. The simulations show that, on average, the approximate algorithm preempts bandwidth...