Randomized algorithms
Random sampling in graph optimization problems
Random sampling in graph optimization problems
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
On-line algorithms for Steiner tree problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
A better approximation ratio for the minimum k-edge-connected spanning subgraph problem
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Resource optimization in QoS multicast routing of real-time multimedia
IEEE/ACM Transactions on Networking (TON)
Iterative rounding 2-approximation algorithms for minimum-cost vertex connectivity problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the approximability of some network design problems
ACM Transactions on Algorithms (TALG)
Algorithms for Single-Source Vertex Connectivity
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
An O(k^3 log n)-Approximation Algorithm for Vertex-Connectivity Survivable Network Design
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Combining Exact and Heuristic Approaches for the Capacitated Fixed-Charge Network Flow Problem
INFORMS Journal on Computing
Minimum-Cost Network Design with (Dis)economies of Scale
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Multicast routing for energy minimization using speed scaling
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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In the capacitated survivable network design problem (Cap-SNDP), we are given an undirected multi-graph where each edge has a capacity and a cost. The goal is to find a minimum cost subset of edges that satisfies a given set of pairwise minimum-cut requirements. Unlike its classical special case of SNDP when all capacities are unit, the approximability of Cap-SNDP is not well understood; even in very restricted settings no known algorithm achieves a o(m) approximation, where m is the number of edges in the graph. In this paper, we obtain several new results and insights into the approximability of Cap-SNDP. We give an O(log n) approximation for a special case of Cap-SNDP where the global minimum cut is required to be at least R, by rounding the natural cut-based LP relaxation strengthened with valid knapsackcover inequalities. We then show that as we move away from global connectivity, the single pair case (that is, when only one pair (s, t) has positive connectivity requirement) captures much of the difficulty of Cap-SNDP: even strengthened with KC inequalities, the LP has an Ω(n) integrality gap. Furthermore, in directed graphs, we show that single pair Cap-SNDP is 2log1-δn-hard to approximate for any fixed constant δ 0. We also consider a variant of the Cap-SNDP in which multiple copies of an edge can be bought: we give an O(log k) approximation for this case, where k is the number of vertex pairs with non-zero connectivity requirement. This improves upon the previously known O(min{k, log Rmax})-approximation for this problem when the largest minimumcut requirement, namely Rmax, is large. On the other hand, we observe that the multiple copy version of Cap-SNDP is Ω(log log n)-hard to approximate even for the single-source version of the problem.