Greedy Online Algorithms for Routing Permanent Virtual Circuits

We analyze the competitive ratio of two greedy online algorithms for routing permanent virtual circuits in a network with arbitrary topology and uniform capacity links. We show that the competitive ratio of the first algorithm, with respect to network congestion, is in \Omega\Gamma p Dm) and O( p DLm), where m is the number of links in the network, D is the maximum ratio, over all requests, of the length of the longest path for the request to the length of the shortest path for the request, and L is the ratio of the maximum to minimum bandwidth requirement. We show that the competitive ratio of the second greedy algorithm is in \Omega\Gamma d + log(n \Gamma d)) and min n O(d log n); O( p DLm) o when the optimal route assignment is pairwise edge disjoint, where n is the number of network nodes and d is the length of the longest path that can be assigned to a request. It is known that the optimal competitive ratio for this problem is \Theta(log n). Aspnes, et al. [1, 2] designed a..