New bounds on the classical and quantum communication complexity of some graph properties

Leibniz International Proceedings in Informatics, LIPIcs

Volumn 18, Issue , 2012, Pages 148-159

  Ivanyos, Gábor ^a   Klauck, Hartmut ^b,c   Lee, Troy ^b   Santha, Miklos ^b,d   De Wolf, Ronald ^e  

^a INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^d UNIVERSITÉ PARIS DIDEROT   (France)

^e UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Communication complexity; Graph properties; Quantum communication

Indexed keywords

BIPARTITE GRAPHS; COMMUNICATION COMPLEXITY; DISTRIBUTED MATRIX; GRAPH PROBLEMS; GRAPH PROPERTIES; PERFECT MATCHINGS; QUANTUM COMMUNICATION COMPLEXITY; QUANTUM LOWER BOUNDS;

COMMUNICATION; GRAPH THEORY; SOFTWARE ENGINEERING;

QUANTUM COMMUNICATION;

EID: 84880220394     PISSN: 18688969     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.4230/LIPIcs.FSTTCS.2012.148     Document Type: Conference Paper

References (33)

1. S. Aaronson and A. Ambainis. Quantum search of spatial regions. Theory of Computing, 1(1):47-79, 2005. Earlier version in FOCS'03. quant-ph/0303041.
2. L. Babai, P. Frankl, and J. Simon. Complexity classes in communication complexity theory. In Proceedings of 27th IEEE FOCS, pages 337-347, 1986.
3. H. Buhrman, R. Cleve, and A. Wigderson. Quantum vs. classical communication and computation. In Proceedings of 30th ACM STOC, pages 63-68, 1998. quant-ph/9802040.
4. A. Chakrabarti and S. Khot. Improved lower bounds on the randomized complexity of graph properties. Random Structures and Algorithms, 30(3):427-440, 2007. Earlier in ICALP'01.
5. R. Cleve, W. van Dam, M. Nielsen, and A. Tapp. Quantum entanglement and the communication complexity of the inner product function. In Proceedings of 1st NASA QCQC conference, volume 1509 of LNCS, 61-74. Springer, 1998. quant-ph/9708019.
6. D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251-280, 1990. Earlier version in STOC'87.
7. A. DasSarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai, G. Pandurangan, D. Peleg, and R. Wattenhofer. Distributed verification and hardness of distributed approximation. In Proceedings of 43rd ACM STOC, pages 363-372, 2011.
8. P. Duris and P. Pudlák. On the communication complexity of planarity. In Proceedings of 7th Fundamentals of Computation Theory (FCT'89), pages 145-147, 1989.
9. C. Dürr, M. Heiligman, P. Høyer, and M. Mhalla. Quantum query complexity of some graph problems. SIAM Journal on Computing, 35(6):1310-1328, 2006. Earlier in ICALP'04.
10. M. Elkin, H. Klauck, D. Nanongkai, and G. Pandurangan. Quantum distributed network computing: Lower bounds and techniques. Manuscript, 2012.
11. J. Forster. A linear lower bound on the unbounded error probabilistic communication complexity. In Proc. of 16th IEEE Conf. on Computational Complexity, 100-106, 2001.
12. A. Hajnal, W. Maass, and G. Turán. On the communication complexity of graph properties. In Proceedings of 20th ACM STOC, pages 186-191, 1988.
13. 4/3 lower bound on the randomized complexity of graph properties. Combinatorica, 11:131-143, 1991. Earlier version in Structures'90.
14. M. R. Henzinger and M. L. Fredman. Lower bounds for fully dynamic connectivity problems in graphs. Algorithmica, 22(3):351-362, 1998.
15. 5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal on Computing, 2(4):225-231, 1973. Earlier version in FOCS'71.
16. B. Kalyanasundaram and G. Schnitger. The probabilistic communication complexity of set intersection. SIAM Journal on Discrete Mathematics, 5(4):545-557, 1992.
17. I. Kremer. Quantum communication. Master's thesis, Hebrew University, CS Dept., 1995.
18. E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge Univ Press, 1997.
19. T. Lee and S. Zhang. Composition theorems in communication complexity. In Proceedings of the 37th ICALP, pages 475-489, 2010. arXiv:1003.1443.
20. L. Lovász. On determinants, matchings, and random algorithms. In Proceedings of 2nd Fundamentals of Computation Theory (FCT'79), pages 565-574, 1979.
21. M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
22. C. H. Papadimitriou and M. Sipser. Communication complexity. Journal of Computer and System Sciences, 28(2):260-269, 1984. Earlier version in STOC'82.
23. A. Razborov. On the distributional complexity of disjointness. Theoretical Computer Science, 106(2):385-390, 1992.
24. A. Razborov. Quantum communication complexity of symmetric predicates. Izvestiya of the Russian Academy of Sciences, mathematics, 67(1):159-176, 2003. quant-ph/0204025.
25. R. Rivest and S. Vuillemin. On recognizing graph properties from adjacency matrices. Theoretical Computer Science, 3:371-384, 1976.
26. J. T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. Journal of the ACM, 27:701-717, 1980.
27. A. Stothers. On the Complexity of Matrix Multiplication. PhD thesis, University of Edinburgh, 2010.
28. X. Sun and C. Wang. Randomized communication complexity for linear algebra problems over finite fields. In Proceedings of 29th Annual Symposium on Theoretical Aspects of Computer Science (STACS'2012), pages 477-488, 2012.
29. X. Sun, C. Wang, and W. Yu. The relationship between inner product and counting cycles. In Proceedings of LATIN'2012, pages 643-654, 2012.
30. L. Valiant. Completeness classes in algebra. In Proc. of 11th ACM STOC, 249-261, 1979.
31. V. Vassilevska Williams. Multiplying matrices faster than Coppersmith-Winograd. In Proceedings of 44th ACM STOC, pages 887-898, 2012.
32. R. de Wolf. Quantum communication and complexity. Theoretical Computer Science, 287(1):337-353, 2002.
33. R. E. Zippel. Probabilistic algorithms for sparse polynomials. In Proceedings of EUROSAM 79, volume 72 of Lecture Notes in Computer Science, pages 216-226, 1979.