Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Randomized algorithms
The hop-limit approach for spare-capacity assignment in survivable networks
IEEE/ACM Transactions on Networking (TON)
Optimal capacity placement for path restoration in STM or ATM mesh-survivable networks
IEEE/ACM Transactions on Networking (TON)
Algorithms for Restoration Planning in a Telecommunications Network
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
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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+驴, 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 + 驴)-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(m2|G|) 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+驴)- approximation algorithm that requires only the solution of a linear program with O(m) commodities, and hence O(m2) 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 + 驴 and 4 + 驴, respectively.