Approximation Algorithms for Restoration Capacity Planning

Abstract

Amajor task of telecommunication network planners is deciding where spare capacity is needed, and howmuch, so that interrupted traffic may be rerouted in the event of a failure. Planning the spare capacity so as to minimize cost is an NP-hard problem, and for large networks, even the linear relaxation is too large to be solved with existing methods. The main contribution of this paper is a fast algorithm for restoration capacity planning with a proven performance ratio of at most 2+∈, and which generates solutions that are at most 1% away from optimal in empirical studies on a range of networks, with up to a few hundred nodes.

As a preliminary step, we present the first (1 + ∈)-approximation algorithm for restoration capacity planning. The algorithm could be practical for moderate-size networks. It requires the solution of a multicommodity-flow type linear program with O(m|G|) commodities, however, where G is the set of distinct traffic routes, and therefore O(m2jGj) variables. For many networks of practical interest, this results in programs too large to be handled with current linear programming technology. Our second result, therefore, has greater practical relevance: a (2+∈)- approximation algorithm that requires only the solution of a linear program with O(m) commodities, and hence O(m ²) variables. The linear program has been of manageable size for all practical telecommunications network instances that have arisen in the authors’ applications, and we present an implementation of the algorithm and an experimental evaluation showing that it is within 1% of optimal on a range of networks arising practice.

We also consider a more general problem in which both service and restoration routes are computed together. Both approximation algorithms extend to this case, with approximation ratios of 1 + ∈ and 4 + ∈, respectively.