Lower bounds for local search by quantum arguments

Conference Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2004, Pages 465-474

  Aaronson, Scott ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Decision tree); Local optima; Local search; PLS; Quantum computing; Query complexity (black box

Indexed keywords

ALGORITHMS; BOOLEAN FUNCTIONS; COMPUTATIONAL COMPLEXITY; DATA PROCESSING; PROBLEM SOLVING;

LOCAL OPTIMA; LOCAL SEARCH; QUANTUM COMPUTING; QUERY COMPLEXITY;

QUANTUM THEORY;

EID: 4544265136     PISSN: 07349025     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1007352.1007358     Document Type: Conference Paper

References (24)

1. S. Aaronson. Quantum lower bound for the collision problem, Proc. ACM STOC, pp. 635-642, 2002. quant-ph/0111102.
2. D. Aharonov and O. Regev. Approximating the shortest and closest vector in a lattice to within √ are in NP ∩ coNP, unpublished.
3. D. Aldous. Minimization algorithms and random walk on the d-cube, Annals of Probability 11(2):403-413, 1983.
4. A. Ambainis. Polynomial degree vs. quantum query complexity, Proc. IEEE FOCS, pp. 230-239, 2003. quant-ph/0305028.
5. A. Ambainis. Quantum lower bounds by quantum arguments, J. Comput. Sys. Sci. 64:750-767, 2002. Earlier version in STOC 2000. quant-ph/0002066.
6. A. Ambainis. Quantum lower bounds by quantum arguments, J. Comput. Sys. Sci. 64:750-767, 2002. Earlier version in STOC 2000. quant-ph/0002066.
7. T. Baker, J. Gill, and R. Solovay. Relativizations of the P=?NP question, SIAM J. Comput. 4:431-442, 1975.
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. Earlier version in FOCS 1998. quant-ph/9802049.
9. R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials, J. ACM 48(4):778-797, 2001. Earlier version in FOCS 1998. quant-ph/9802049.
10. C. Bennett, E. Bernstein, G. Brassard, and U. Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comput 26(5):1510-1523, 1997. quant-ph/9701001.
11. H. Buhrman, R. Cleve, R. de Wolf, and Ch. Zalka. Bounds for small-error and zero-error quantum algorithms, Proc. IEEE FOCS, pp. 358-368, 1999. cs.CC/9904019.
12. H. Buhrman and R. de Wolf. Complexity measures and decision tree complexity: a survey, Theoretical Comput. Sci. 288:21-43, 2002.
13. R. Diestel. Graph Theory (2nd edition), Springer-Verlag, 2000.
14. S. Droste, T. Jansen, and I. Wegener. Upper and lower bounds for randomized search heuristics in black-box optimization, ECCC TR03-048, 2003.
15. C. Dürr and P. Høyer. A quantum algorithm for finding the minimum, 1996. quant-ph/9607014.
16. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem, Science 292:472-476, 2001. quant-ph/0104129.
17. D. S. Johnson, C. H. Papadimitriou, and M. Yannakakis. How easy is local search?, J. Comput. Sys. Sci. 37:79-100, 1988.
18. I. Kerenidis and R. de Wolf, Exponential lower bound for 2-query locally decodable codes via a quantum argument, Proc. ACM STOC, pp. 106-115, 2003. quant-ph/0208062.
19. D. C. Llewellyn and C. Tovey. Dividing and conquering the square, Discrete Appl. Math 43:131-153, 1993.
20. D. C. Llewellyn, C. Tovey, and M. Trick. Local optimization on graphs, Discrete Appl. Math 23:157-178, 1989. Erratum: 46:93-94, 1993.
21. N. Megiddo and C. H. Papadimitriou. On total functions, existence theorems, and computational complexity, Theoret. Comp. Sci. 81:317-324, 1991.
22. C. H. Papadimitriou. Talk at UC Berkeley, February 6, 2003.
23. M. Santha and M. Szegedy. Quantum and classical query complexities of local search are polynomially related, this Proceedings, 2004.
24. Y. Shi. Quantum lower bounds for the collision and the element distinctness problems, Proc. IEEE FOCS, pp. 513-519, 2002. quant-ph/0112086.