An optimal lower bound on the communication complexity of Gap-Hamming-Distance

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2011, Pages 51-60

  Chakrabarti, Amit ^a   Regev, Oded ^b,c  

^a Dartmouth Department of Computer Science_Dartmouth College   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

communication complexity; corruption; data streams; gap hamming distance; gaussian noise correlation; lower bounds

Indexed keywords

COMPUTATIONAL COMPLEXITY; DATA STREAMS; FREQUENCY ESTIMATION; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC);

COMMUNICATION COMPLEXITY; CORRUPTION; GAP HAMMING DISTANCES; GAUSSIAN NOISE CORRELATIONS; LOWER BOUNDS;

HAMMING DISTANCE;

EID: 79959768278     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1993636.1993644     Document Type: Conference Paper

References (36)

1. C. J. Arackaparambil, J. Brody, and A. Chakrabarti. Functional monitoring without monotonicity. In Proc. 36th International Colloquium on Automata, Languages and Programming, pages 95-106. 2009.
2. F. Barthe. An isoperimetric result for the Gaussian measure and unconditional sets. Bull. London Math. Soc., 33(4):408-416, 2001.
3. J. Brody and A. Chakrabarti. A multi-round communication lower bound for gap hamming and some consequences. In Proc. 24th Annual IEEE Conference on Computational Complexity, pages 358-368. 2009.
4. J. Brody, A. Chakrabarti, O. Regev, T. Vidick, and R. de Wolf. Better gap-hamming lower bounds via better round elimination. In Proc. 14th International Workshop on Randomization and Approximation Techniques in Computer Science. 2010.
5. H. Buhrman, R. Cleve, and A. Wigderson. Quantum vs. classical communication and computation. In Proc. 30th Annual ACM Symposium on the Theory of Computing, pages 63-68. 1998.
6. S. G. Bobkov. On concentration of distributions of random weighted sums. Ann. Probab., 31(1):195-215, 2003.
7. C. Borell. Geometric bounds on the Ornstein-Uhlenbeck velocity process. Z. Wahrsch. Verw. Gebiete, 70(1):1-13, 1985.
8. P. Beame, T. Pitassi, N. Segerlind, and A. Wigderson. A strong direct product theorem for corruption and the multiparty communication complexity of disjointness. Comput. Complexity, 15(4):391-432, 2006.
9. A. Chakrabarti, G. Cormode, and A. McGregor. A near-optimal algorithm for computing the entropy of a stream. In Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 328-335. 2007.
10. P. Diaconis and D. Freedman. Asymptotics of graphical projection pursuit. Ann. Statist., 12(3):793-815, 1984.
11. R. M. Gray. Entropy and Information Theory. Springer-Verlag, New York, NY, USA, 1990. Available online at http://ee.stanford.edu/~gray/it.html.
12. P. Indyk and D. Woodruff. Tight lower bounds for the distinct elements problem. In Proc. 45th Annual IEEE Symposium on Foundations of Computer Science, pages 283-289. 2003.
13. R. Jain and H. Klauck. The partition bound for classical communication complexity and query complexity. In Proc. 25th Annual IEEE Conference on Computational Complexity, pages 247-258. 2010.
14. T. S. Jayram, R. Kumar, and D. Sivakumar. The one-way communication complexity of gap hamming distance, 2007. Manuscript.
15. H. Klauck. Rectangle size bounds and threshold covers in communication complexity. In Proc. 18th Annual IEEE Conference on Computational Complexity, pages 118-134. 2003.
16. B. Klartag. A central limit theorem for convex sets. Invent. Math., 168(1):91-131, 2007.
17. H. Klauck. A strong direct product theorem for disjointness. In Proc. 41st Annual ACM Symposium on the Theory of Computing, pages 77-86. 2010.
18. E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, Cambridge, 1997.
19. D. M. Kane, J. Nelson, and D. P. Woodruff. An optimal algorithm for the distinct elements problem. In Proc. 29th ACM Symposium on Principles of Database Systems, pages 41-52. 2010.
20. M. Karchmer and A. Wigderson. Monotone circuits for connectivity require super-logarithmic depth. SIAM J. Disc. Math., 3(2):255-265, 1990.
21. Preliminary version in Proc. 20th Annual ACM Symposium on the Theory of Computing, pages 539-550, 1988.
22. N. Linial and A. Shraibman. Lower bounds in communication complexity based on factorization norms. In Proc. 39th Annual ACM Symposium on the Theory of Computing, pages 699-708. 2007.
23. P. B. Miltersen, N. Nisan, S. Safra, and A. Wigderson. On data structures and asymmetric communication complexity. J. Comput. Syst. Sci., 57(1):37-49, 1998.
24. Preliminary version in Proc. 27th Annual ACM Symposium on the Theory of Computing, pages 103-111, 1995.
25. A. Nayak and F. Wu. The quantum query complexity of approximating the median and related statistics. In Proc. 31st Annual ACM Symposium on the Theory of Computing, pages 384-393. 1999.
26. M. Pǎtraşcu. (Data) STRUCTURES. In Proc. 49th Annual IEEE Symposium on Foundations of Computer Science, pages 434-443. 2008.
27. A. A. Razborov. On the distributional complexity of disjointness. Theoretical Computer Science, 106(2):385-390, 1992.
28. Preliminary version in Proc. 17th International Colloquium on Automata, Languages and Programming, pages 249-253, 1990.
29. R. Raz. Exponential separation of quantum and classical communication complexity. In Proc. 31st Annual ACM Symposium on the Theory of Computing, pages 358-367. 1999.
30. A. A. Razborov. Quantum communication complexity of symmetric predicates. Izvestiya of the Russian Academy of Science, Mathematics, 67:0204025, 2002.
31. A. A. Sherstov. The pattern matrix method for lower bounds on quantum communication. In Proc. 40th Annual ACM Symposium on the Theory of Computing, pages 85-94. 2008.
32. V. N. Sudakov. Typical distributions of linear functionals in finite-dimensional spaces of high dimension. Dokl. Akad. Nauk SSSR, 243(6):1402-1405, 1978.
33. T. Vidick. A concentration inequality for the overlap of a vector on a large set, with application to communication complexity, 2010. Manuscript.
34. D. P. Woodruff. Optimal space lower bounds for all frequency moments. In Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 167-175. 2004.
35. D. P. Woodruff. Efficient and Private Distance Approximation in the Communication and Streaming Models. Ph.D. thesis, MIT, 2007.
36. D. Woodruff. The average case complexity of counting distinct elements. In Proc. 12th International Conference on Database Theory, pages 284-295. 2009.