Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
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
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Interval selection: applications, algorithms, and lower bounds
Journal of Algorithms
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximation Algorithms for the Job Interval Selection Problem and Related Scheduling Problems
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Journal of Computer and System Sciences
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Machine Minimization for Scheduling Jobs with Interval Constraints
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the undirected congestion minimization problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Logarithmic hardness of the directed congestion minimization problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Resource Minimization Job Scheduling
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms and hardness of integral concurrent flow
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We study the approximability of two natural NP-hard problems. The first problem is congestion minimization in directed networks. In this problem, we are given a directed graph and a set of source-sink pairs. The goal is to route all the pairs with minimum congestion on the network edges. The second problem is machine scheduling, where we are given a set of jobs, and for each job, there is a list of intervals on which it can be scheduled. The goal is to find the smallest number of machines on which all jobs can be scheduled such that no two jobs overlap in their execution on any machine. Both problems are known to be O(log n/log log n)-approximable via the randomized rounding technique of Raghavan and Thompson [1987]. However, until recently, only Max SNP hardness was known for each problem. We make progress in closing this gap by showing that both problems are Ω(log log n)-hard to approximate unless NP ⊆ DTIME(nO(log log log n)).