On the black-box complexity of Sperner's Lemma

Lecture Notes in Computer Science

Volumn 3623, Issue , 2005, Pages 245-257

  Friedl, Katalin ^a   Ivanyos, Gábor ^b   Santha, Miklos ^c   Verhoeven, Yves F ^c,d  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b INSTITUTE FOR COMPUTER SCIENCE AND CONTROL   (Hungary)

^c CNRS   (France)

^d TELECOM PARISTECH   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; GRAPH THEORY; PROBABILITY;

BLACK-BOX COMPLEXITY; QUANTUM QUERY COMPLEXITY; SPERNER PROBLEMS;

COMPUTER SCIENCE;

EID: 26844469424     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11537311_22     Document Type: Conference Paper

References (26)

1. S. Aaronson. Quantum lower bound for the collision problem. In 34th STOC, pp. 635-642, 2002.
2. S. Aaronson. Lower bounds for local search by quantum arguments. In 36th STOC, pp. 465-474, 2004.
3. A. Ambainis. Polynomial degree vs. quantum query complexity. In 44th FOCS, pp. 230-239, 2003.
4. R. Beals, H. Buhrman, R. Cleve, M. Mosca and R. de Wolf. Quantum lower bounds by polynomials, J. of the ACM (48):4, pp. 778-797, 2001.
5. P. Beame, S. Cook, J. Edmonds, R. Impagliazzo and T. Pitassi. The relative complexity of NP search problems. J. Comput. System Sci., 57(1):3-19, 1998.
6. C. Bennett, E. Bernstein, G. Brassard and U. Vazirani. Strength and weaknesses of quantum computing. SIAM J. on Computing, 26(5):1510-1523, 1997.
7. E. Bloch. Mod 2 degree and a generalized no retraction Theorem. To appear in Mathematische Nachrichten.
8. J. Buresh-Oppenheim and T. Morioka. Relativized NP search problems and prepositional proof systems. In 19th Conference on Computational Complexity, pp. 54-67, 2004.
9. P. Crescenzi and R. Silvestri. Sperner's lemma and robust machines. Comput. Complexity, 7(2):163-173, 1998.
10. D. Deutsch and R. Jozsa. Rapid solution of problems by quantum computation. Proc. of the Royal Society A, volume 439,1985.
11. m with the octahedral triangulation. J. Combinatorial Theory, 2:588-602, 1967.
12. K. Friedl, Gábor Ivanyos, Miklos Santha and Yves Verhoeven. On the black-box complexity of Sperner's Lemma, http://xxx.lanl.gov/abs/quant-ph/ 0505185.
13. J. Gilbert, J. Hutchinson and R. Tarjan. A separator theorem for graphs of bounded genus. J. Algorithms, 5(3):391-407, 1984.
14. S. Laplante and F. Magniez. Lower bounds for randomized and quantum query complexity using kolmogorov arguments. In 19th Conference on Computational Complexity, pp. 294-304, 2004.
15. D. Llewellyn and C. Tovey. Dividing and conquering the square. Discrete Appl. Math., 43(2):131-153, 1993.
16. D. Llewellyn, C. Tovey and M. Trick. Local optimization on graphs. Discrete Appl. Math., 23(2): 157-178, 1989.
17. N. Megiddo and C. Papadimitriou. On total functions, existence theorems and computational complexity. Theoret. Comput. Sci., 81:317-324, 1991.
18. C. Papadimitriou. On graph-theoretic lemmata and complexity classes. In 31st FOCS, pp. 794-801, 1990.
19. C. Papadimitriou. On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. System Sci., 48(3):498-532, 1994.
20. M. Santha and M. Szegedy. Quantum and classical query complexities of local search are polynomially related. In 36th STOC, pp. 494-501, 2004.
21. Y. Shi. Quantum lower bounds for the collision and the element distinctness problems. In 43rd FOCS, pp. 513-519, 2002.
22. D. Simon. On the power of quantum computation. SIAM J. on Computing (26):5, pp. 1474-1783, 1997.
23. E. Sperner. Neuer Beweis für die Invarianz der Dimensionzahl und des Gebietes. Abh. Math. Sem. Hamburg Univ. 6:265-272, 1928.
24. R. Špalek and M. Szegedy. All quantum adversary methods are equivalent, http://xxx.lanl.gov/abs/quant-ph/0409116.
25. L. Taylor. Sperner's Lemma, Brouwer's Fixed Point Theorem, The Fundamental Theorem of Algebra, http://www.cs.csubak.edu/~larry/math/sperner. pdf.
26. A. Thomason. Hamilton cycles and uniquely edge colourable graphs. Ann. Discrete Math. 3: 259-268, 1978.