Matthew Andrews
ABSTRACT
We show that for any constant ε > 0, there is no Ω(log1-εM)-approximation algorithm for the directed congestion minimization problem on networks of size M unless NP ⊆ ZPTIME(npolylog n). This bound is almost tight given the O(log M/ log log M)-approximation via randomized rounding due to Raghavan and Thompson.
- M. Andrews, J. Chuzhoy, S. Khanna, and L. Zhang. Hardness of the undirected edge-disjoint paths problem with congestion. In Proceedings of the 46th Annual Symposium on Foundations of Computer Science, Pittsburgh, PA, October 2005. Google Scholar
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- M. Andrews and L. Zhang. Hardness of the undirected congestion minimization problem. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, May 2005. Google ScholarDigital Library
- S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. Journal of the ACM, 45(3):501--555, 1998. Google ScholarDigital Library
- J. Chuzhoy and J. Naor. New hardness results for congestion minimization and machine scheduling. In Proceedings of the 36th Annual ACM Symposium of Theory of Computing, pages 28 -- 34, Chicago, IL, 2004. Google ScholarDigital Library
- V. Guruswami, S. Khanna, R. Rajaraman, B. Shepherd, and M. Yannakakis. Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems. In Proceedings of the 31st Annual ACM Symposium of Theory of Computing, pages 19--28, Atlanta, GA, May 1999. Google ScholarDigital Library
- R.M. Karp. Reducibility among combinatorial problems. In R.E. Miller and J.W. Thatcher, editors, Complexity of Computer Computations, pages 85 -- 103, 1972.Google ScholarCross Ref
- T. Leighton, S. Rao, and A. Srinivasan. Multicommodity flow and circuit switching. In Proceedings of the 31st Annual Hawaii International Conference on System Sciences, pages 459--465, 1998. Google ScholarDigital Library
- M. Martens and M. Skutella. Flows on few paths: Algorithms and lower bounds. In Proceedings of the 12th Annual European Symposium on Algorithms, pages 520--531, 2004.Google ScholarCross Ref
- P. Raghavan and C.D. Thompson. Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365 -- 374, 1991. Google ScholarDigital Library
- R. Raz. A parallel repetition theorem. SIAM Journal on Computing, 27(3):763--803, 1998. Google ScholarDigital Library
Index Terms
- Logarithmic hardness of the directed congestion minimization problem
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