Integer and combinatorial optimization
Integer and combinatorial optimization
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Bicriteria network design problems
Journal of Algorithms
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Improved non-approximability results for minimum vertex cover with density constraints
Theoretical Computer Science
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A deterministic algorithm for the cost-distance problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A constant factor approximation for the single sink edge installation problems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximating the Single-Sink Link-Installation Problem in Network Design
SIAM Journal on Optimization
A Constant-Factor Approximation Algorithm for the Multicommodity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Integrated Logistics: Approximation Algorithms Combining Facility Location and Network Design
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
On Network Design Problems: Fixed Cost Flows and the Covering Steiner Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Primal-Dual Algorithms for Connected Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation Algorithms for the Traveling Purchaser Problem and its Variants in Network Design
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Resource optimization in QoS multicast routing of real-time multimedia
IEEE/ACM Transactions on Networking (TON)
Online algorithms for network design
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Hardness of Buy-at-Bulk Network Design
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Video distribution on multicast networks
IEEE Journal on Selected Areas in Communications
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Approximation algorithms for node-weighted buy-at-bulk network design
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Stochastic Steiner Tree with Non-uniform Inflation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
On capacitated set cover problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating buy-at-bulk and shallow-light k-Steiner trees
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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Consider the following classical network design problem: a set of terminals T = [ti wants to send traffic to a "root" r in an n-node graph G = (V,E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some base capacity ue --- and hence provisioning k x ue bandwidth on edge e incurs a cost of [k] times the cost of that edge. The objective is a minimum-cost feasible solution.This is one of many network design problems widely studied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables to be purchased on them, or certain quality-of-service requirements may have to be met.In this work, we show that the above problem, and in fact, several basic problems in this general network design framework, cannot be approximated better than Ω(log log n) unless NP ⊆ DTIME (nO(log log log n). In particular, we show that this inapproximability threshold holds for (i) the Priority-Steiner Tree problem [7], (ii) the Cost-Distance problem [31], and the single-sink version of an even more fundamental problem, (iii) Fixed Charge Network Flow [33]. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first non-constant hardness results known for all these problems.