Greedy online algorithms for routing permanent virtual circuits

Abstract

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 ⍀( ͌ Ᏸm) and O( ͌ Ᏸᏸm), where m is the number of links in the network, Ᏸ 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 ᏸ is the ratio of the maximum-tominimum bandwidth requirement. We show that the competitive ratio of the second greedy algorithm is in ⍀(d ϩ log(n Ϫ d)) and min{O(d log n), O( ͌ Ᏸᏸm)} 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 ⌰(log n). Aspnes et al. designed a ⌰(log n) competitive online algorithm that computes an exponential function of current congestion to make each decision. The greedy online algorithms, although not optimal, make each decision more quickly and still have good competitive ratios in many nontrivial situations.