Online and stochastic survivable network design

Consider the edge-connectivity survivable network design problem: given a graph G = (V, E) with edge-costs, and edgeconnectivity requirements rij Z0 for every pair of vertices i, j V , find an (approximately) minimum-cost network that provides the required connectivity. While this problem is known to admit good approximation algorithms in the offline case, no algorithms were known for this problem in the online setting. In this paper, we give a randomized O(rmax log3 n) competitive online algorithm for this edge-connectivity network design problem, where rmax = maxij rij. Our algorithms use the standard embeddings of graphs into random subtrees (i.e., into singly connected subgraphs) as an intermediate step to get algorithms for higher connectivity. Our results for the online problem give us approximation algorithms that admit strict cost-shares with the same strictness value. This, in turn, implies approximation algorithms for (a) the rent-or-buy version and (b) the (twostage) stoc...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Anupam Gupta, Ravishankar Krishnaswamy, R. Ravi
• Keywords: Algorithms, Approximation Algorithms, Network Design Problem, STOC 2009, Stochastic Algorithms