Lower bounds for local search by quantum arguments

SIAM Journal on Computing

Volumn 35, Issue 4, 2006, Pages 804-824

  Aaronson, Scott ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Decision trees; Local optima; Local search; Polynomial local search; Quantum computing; Query complexity; Random walks

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DECISION MAKING; PROBLEM SOLVING; TREES (MATHEMATICS);

DECISION TREES; LOCAL OPTIMA; LOCAL SEARCH; POLYNOMIAL LOCAL SEARCH; QUANTUM COMPUTING; QUERY COMPLEXITY; RANDOM WALKS;

QUANTUM THEORY;

EID: 33747170669     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539704447237     Document Type: Conference Paper

References (29)

1. S. AARONSON, Quantum lower bound for the collision problem, in Proceedings of ACM STOC, 2002, pp. 635-642 (quant-ph/0111102).
2. D. AHARONOV AND O. REGEV, Lattice problems in NP intersect coNP, in Proceedings of IEEE FOCS, 2004, pp. 362-371.
3. D. ALDOUS, Minimization algorithms and random walk on the d-cube, Ann. Probab., 11 (1983), pp. 403-413.
4. A. AMBAINIS, Quantum lower bounds by quantum arguments, J. Comput. System Sci., 64 (2002), pp. 750-767
5. (earlier version in ACM STOC 2000, quant-ph/0002066).
6. A. AMBAINIS, Polynomial degree vs. quantum query complexity, in Proceedings of IEEE FOCS, 2003, pp. 230-239 (quant-ph/0305028).
7. T. BAKER, J. GILL, AND R. SOLOVAY, Relativizations of the P=?NP question, SIAM J. Comput., 4 (1975), pp. 431-442.
8. R. BEALS, H. BUHRMAN, R. CLEVE, M. MOSCA, AND R. DE WOLF, Quantum lower bounds by polynomials, J. ACM, 48 (2001), pp. 778-797
9. (earlier version in IEEE FOCS 1998, pp. 352-361, quant-ph/9802049).
10. C. H. BENNETT, E. BERNSTEIN, G. BRASSARD, AND U. VAZIRANI, Strengths and weaknesses of quantum computing, SIAM J. Comput., 26 (1997), pp. 1510-1523 (quant-ph/9701001).
11. H. BUHRMAN AND R. DE WOLF, Complexity measures and decision tree complexity: A survey, Theoret. Comput. Sci., 288 (2002), pp. 21-43.
12. R. DIESTEL, Graph Theory, 2nd ed., Springer-Verlag, New York, 2000.
13. S. DROSTE, T. JANSEN, AND I. WEGENER, Upper and lower bounds for randomized search heuristics in black-box optimization, Theory Comput. Syst., to appear.
14. C. DÜRR AND P. HØYER, A quantum algorithm for finding the minimum, 1996 (quant-ph/9607014).
15. 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 (2001), pp. 472-476 (quant-ph/0104129).
16. D. S. JOHNSON, C. H. PAPADIMITRIOU, AND M. YANNAKAKIS, How easy is local search?, J. Comput. System Sci., 37 (1988), pp. 79-100.
17. I. KERENIDIS AND R. DE WOLF, Exponential lower bound for 2-query locally decodable codes via a quantum argument, in Proceedings of ACM STOC, 2003, pp. 106-115 (quant-ph/0208062).
18. S. LAPLANTE AND F. MAGNIEZ, Lower bounds for randomized and quantum query complexity using Kolmogorov arguments, in Proceedings of IEEE Conference on Computational Complexity, 2004, pp. 294-304 (quant-ph/0311189).
19. D. C. LLEWELLYN AND C. TOVEY, Dividing and conquering the square, Discrete Appl. Math., 43 (1993), pp. 131-153.
20. D. C. LLEWELLYN, C. TOVEY, AND M. TRICK, Local optimization on graphs, Discrete Appl. Math., 23 (1989), pp. 157-178.
21. D. C. LLEWELLYN, C. TOVEY, AND M. TRICK, Erratum: Local optimization on graphs, Discrete Appl. Math., 46 (1993), pp. 93-94.
22. N. MEGIDDO AND C. H. PAPADIMITRIOU, On total functions, existence theorems, and computational complexity, Theoret. Comput. Sci., 81 (1991), pp. 317-324.
23. R. MOTWANI AND P. RAGHAVAN, Randomized Algorithms, Cambridge University Press, Cambridge, UK, 1995.
24. C. H. PAPADIMITRIOU, talk at UC Berkeley, February 6, 2003.
25. M. SANTHA AND M. SZEGEDY, Quantum and classical query complexities of local search are polynomially related, in Proceedings of ACM STOC, 2004, pp. 494-501.
26. Y. SHI, Quantum lower bounds for the collision and the element distinctness problems, in Proceedings of IEEE FOCS, 2002, pp. 513-519. quant-ph/0112086.
27. Y. VERHOEVEN, Enhanced algorithms for local search, Inform. Process. Lett., to appear (quant-ph/0506019).
28. R. ŠPALEK AND M. SZEGEDY, All quantum adversary methods are equivalent, in Proceedings of the International Colloquium on Automata, Languages, and Programming (ICALP), 2005, pp. 1299-1311 (quant-ph/0409116).
29. S. ZHANG, (Almost) tight bounds for randomized and quantum local search on hypercubes and grids, 2005 (quant-ph/0504085).