The multiparty communication complexity of set disjointness

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2012, Pages 525-544

  Sherstov, Alexander A ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

circuit complexity; direct product theorems; multiparty communication complexity; set disjointness problem

Indexed keywords

CIRCUIT COMPLEXITY; COMMUNICATION COMPLEXITY; DEPTH 3; DIRECT PRODUCT THEOREMS; DISJOINTNESS; DISJOINTNESS PROBLEMS; LOWER BOUNDS; MULTI-PARTY COMMUNICATION; MULTIPARTY COMMUNICATION COMPLEXITY; THREE MODELS;

COMMUNICATION; COMPUTATION THEORY;

PROBLEM SOLVING;

EID: 84862624952     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2213977.2214026     Document Type: Conference Paper

References (51)

1. E. Allender. A note on the power of threshold circuits. In Proceedings of the Thirtieth Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 580-584, 1989.
2. L. Babai. Trading group theory for randomness. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing (STOC), pages 421-429, 1985.
3. L. Babai, P. Frankl, and J. Simon. Complexity classes in communication complexity theory. In Proceedings of the Twenty-Seventh Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 337-347, 1986.
4. L. Babai, T. P. Hayes, and P. G. Kimmel. The cost of the missing bit: Communication complexity with help. Combinatorica, 21(4):455-488, 2001.
5. L. Babai and S. Moran. Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes. J. Comput. Syst. Sci., 36(2):254-276, 1988. (Pubitemid 18623335)
6. L. Babai, N. Nisan, and M. Szegedy. Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs. J. Comput. Syst. Sci., 45(2):204-232, 1992. (Pubitemid 23572023)
7. Z. Bar-Yossef, T. S. Jayram, R. Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci., 68(4):702-732, 2004.
8. R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials. J. ACM, 48(4):778-797, 2001.
9. P. Beame, M. David, T. Pitassi, and P. Woelfel. Separating deterministic from nondeterministic NOF multiparty communication complexity. In Proc. of the 34th International Colloquium on Automata, Languages, and Programming (ICALP), pages 134-145, 2007.
10. P. Beame, M. David, T. Pitassi, and P. Woelfel. Separating deterministic from randomized multiparty communication complexity. Theory of Computing, 6(1):201-225, 2010.
11. P. Beame and D.-T. Huynh-Ngoc. Multiparty communication complexity and threshold circuit complexity of AC0. In Proceedings of the Fiftieth Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 53-62, 2009. Preliminary version in ECCC Report TR08-082, September 2008.
12. P. Beame, T. Pitassi, and N. Segerlind. Lower bounds for Lovász-Schrijver systems and beyond follow from multiparty communication complexity. SIAM J. Comput., 37(3):845-869, 2007.
13. P. Beame, T. Pitassi, N. Segerlind, and A. Wigderson. A strong direct product theorem for corruption and the multiparty communication complexity of disjointness. Computational Complexity, 15(4):391-432, 2006.
14. A. Ben-Aroya, O. Regev, and R. de Wolf. A hypercontractive inequality for matrix-valued functions with applications to quantum computing and LDCs. In Proceedings of the Forty-Ninth Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 477-486, 2008.
15. J. Briet, H. Buhrman, T. Lee, and T. Vidick. Multiplayer XOR games and quantum communication complexity with clique-wise entanglement. Manuscript at http://arxiv.org/abs/0911.4007, 2009.
16. A. K. Chandra, M. L. Furst, and R. J. Lipton. Multi-party protocols. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing (STOC), pages 94-99, 1983.
17. A. Chattopadhyay. Discrepancy and the power of bottom fan-in in depth-three circuits. In Proceedings of the Forty-Eighth Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 449-458, 2007.
18. A. Chattopadhyay. Circuits, Communication, and Polynomials. PhD thesis, McGill University, 2008.
19. A. Chattopadhyay and A. Ada. Multiparty communication complexity of disjointness. In Electronic Colloquium on Computational Complexity (ECCC), January 2008. Report TR08-002.
20. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2):230-261, 1988.
21. M. David and T. Pitassi. Separating NOF communication complexity classes RP and NP. In Electronic Colloquium on Computational Complexity (ECCC), February 2008. Report TR08-014.
22. M. David, T. Pitassi, and E. Viola. Improved separations between nondeterministic and randomized multiparty communication. ACM Transactions on Computation Theory (TOCT), 1(2), 2009.
23. D. Gavinsky and A. A. Sherstov. A separation of NP and coNP in multiparty communication complexity. Theory of Computing, 6(10):227-245, 2010.
24. V. Grolmusz. The BNS lower bound for multi-party protocols in nearly optimal. Inf. Comput., 112(1):51-54, 1994.
25. J. Håstad and M. Goldmann. On the power of small-depth threshold circuits. Computational Complexity, 1:113-129, 1991.
26. R. Jain, H. Klauck, and A. Nayak. Direct product theorems for classical communication complexity via subdistribution bounds. In Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing (STOC), pages 599-608, 2008.
27. B. Kalyanasundaram and G. Schnitger. The probabilistic communication complexity of set intersection. SIAM J. Discrete Math., 5(4):545-557, 1992.
28. H. Klauck. Lower bounds for quantum communication complexity. In Proceedings of the Forty-Second Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 288-297, 2001.
29. H. Klauck. Rectangle size bounds and threshold covers in communication complexity. In Proceedings of the Eighteenth Annual IEEE Conference on Computational Complexity (CCC), pages 118-134, 2003.
30. H. Klauck. A strong direct product theorem for disjointness. In Proceedings of the Forty-Second Annual ACM Symposium on Theory of Computing (STOC), pages 77-86, 2010.
31. H. Klauck, R. Špalek, and R. de Wolf. Quantum and classical strong direct product theorems and optimal time-space tradeoffs. SIAM J. Comput., 36(5):1472-1493, 2007. (Pubitemid 47632456)
32. M. Krause and P. Pudlák. On the computational power of depth-2 circuits with threshold and modulo gates. Theor. Comput. Sci., 174(1-2):137-156, 1997. (Pubitemid 127452780)
33. E. Kushilevitz and N. Nisan. Communication complexity. Cambridge University Press, 1997.
34. T. Lee, G. Schechtman, and A. Shraibman. Lower bounds on quantum multiparty communication complexity. In Proceedings of the Twenty-Fourth Annual IEEE Conference on Computational Complexity (CCC), pages 254-262, 2009.
35. T. Lee and A. Shraibman. Disjointness is hard in the multiparty number-on-the-forehead model. Computational Complexity, 18(2):309-336, 2009. Preliminary version at http://arxiv.org/abs/0712.4279v1, December 2007.
36. N. Linial and A. Shraibman. Lower bounds in communication complexity based on factorization norms. Random Struct. Algorithms, 34(3):368-394, 2009.
37. M. L. Minsky and S. A. Papert. Perceptrons: An Introduction to Computational Geometry. MIT Press, Cambridge, Mass., 1969.
38. N. Nisan and M. Szegedy. On the degree of Boolean functions as real polynomials. Computational Complexity, 4:301-313, 1994.
39. A. A. Razborov. On the distributional complexity of disjointness. Theor. Comput. Sci., 106(2):385-390, 1992.
40. A. A. Razborov. Quantum communication complexity of symmetric predicates. Izvestiya of the Russian Academy of Sciences, Mathematics, 67:145-159, 2002.
41. Ω(log n) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom. Inf. Process. Lett., 45(6):303-307, 1993.
42. A. A. Sherstov. The pattern matrix method for lower bounds on quantum communication. In Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing (STOC), pages 85-94, 2008. Preliminary version in ECCC Report TR07-100, September 2007.
43. A. A. Sherstov. Separating AC0 from depth-2 majority circuits. SIAM J. Comput., 38(6):2113-2129, 2009. Preliminary version in Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing (STOC), 2007.
44. A. A. Sherstov. On quantum-classical equivalence for composed communication problems. Quantum Information & Computation, 10(5-6):435-455, 2010.
45. A. A. Sherstov. Strong direct product theorems for quantum communication and query complexity. In Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (STOC), pages 41-50, 2011. Full version available as ECCC Report TR11-040.
46. Y. Shi and Y. Zhu. Quantum communication complexity of block-composed functions. Quantum Information & Computation, 9(5-6):444-460, 2009.
47. P. Tesson. Computational complexity questions related to finite monoids and semigroups. PhD thesis, McGill University, 2003.
48. E. Viola. Pseudorandom bits for constant-depth circuits with few arbitrary symmetric gates. SIAM J. Comput., 36(5):1387-1403, 2007. (Pubitemid 47632452)
49. E. Viola and A. Wigderson. One-way multiparty communication lower bound for pointer jumping with applications. Combinatorica, 29(6):719-743, 2009.
50. A. C.-C. Yao. Some complexity questions related to distributive computing. In Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing (STOC), pages 209-213, 1979.
51. A. C.-C. Yao. On ACC and threshold circuits. In Proceedings of the Thirty-First Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 619-627, 1990.