Every decision tree has an influential variable

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn 2005, Issue , 2005, Pages 31-39

  O'Donnell, Ryan ^a   Saks, Michael ^b   Schramm, Oded ^a   Servedio, Rocco A ^c  

^a MICROSOFT RESEARCH   (United States)

^b RUTGERS UNIVERSITY   (United States)

^c Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY PRODUCT MEASURE; DECISION TREE; INFLUENTIAL VARIABLE; THRESHOLD PROBABILITY;

BOOLEAN FUNCTIONS; DECISION THEORY; GRAPH THEORY; NUMBER THEORY; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

TREES (MATHEMATICS);

EID: 33748634338     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SFCS.2005.34     Document Type: Conference Paper

References (29)

1. R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf. Quantum lower bounds by polynomials. Journal of the ACM, 48(4):778-797, 2001.
2. M. Ben-Or and N. Linial. Collective coin flipping. In Proceedings of the 26th Annual Symposium on Foundations of Computer Science (FOCS), pages 408-416, 1985.
3. I. Benjamini, O. Schramm, and D. Wilson. Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read. In Proceedings of the 37th Annual Symposium on Theory of Computing (STOC), 2005.
4. M. Best, P. van Emde Boas, and H. Lenstra. A sharpened version of the Aanderaa-Rosenberg conjecture. Technical Report Report ZW30/74, Mathematisch Centrum Amsterdam, 1974.
5. M. Blum and R. Impagliazzo. Generic oracles and oracle classes. In Proceedings of the 28th Annual Symposium on Foundations of Computer Science, pages 118-126, 1987.
6. B. Bollobas. Combinatorics: Set Systems, Hypergraphs, Families of Vectors and Combinatorial Probability. Cambridge University Press, 1986.
7. J. Bourgain and G. Kalai. Influences of variables and threshold intervals under group symmetries. GAFA, 7:438-461, 1997.
8. H. Buhrman and R. de Wolf. Complexity measures and decision tree complexity: a survey. Theoretical Computer Science, 288(1):21-43, 2002.
9. A. Chakrabarti and S. Khot. Improved lower bounds on the randomized complexity of graph properties. In Proceedings of the 28th International Colloquium on Automata, Languages and Programming, pages 285-296, 2001.
10. B. Efron and C. Stein. The jackknife estimate of variance. Annals of Statistics, 9:586-596, 1981.
11. E. Friedgut, J. Kahn, and A. Wigderson. Computing graph properties by randomized subcube partitions. In Proceedings of the 6th International Workshop on Random and Approximation Techniques, pages 105-113, 2002.
12. E. Friedgut and G. Kalai. Every monotone graph property has a sharp threshold. Proceedings of the AMS, 124:2993-3002, 1996.
13. 4/3) lower bound on the randomized complexity of graph properties. Combinatorica, 11:131-143, 1991.
14. J. Kahn, G. Kalai, and N. Linial. The influence of variables on boolean functions. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science, pages 68-80, 1988.
15. V. King. Lower bounds on the complexity of graph properties. In Proceedings of the 20th Annual Symposium on Theory of Computing, pages 468-476, 1988.
16. G. Margulis. Probabilistic characteristics of graphs with large connectivity. Prob. Peredachi Inform., 10:101-108, 1974.
17. E. Mossel, R. O'Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: invariance and optimality. In Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS), 2005.
18. N. Nisan and M. Szegedy. On the degree of Boolean functions as real polynomials. In Proceedings of the Twenty-Fourth Annual Symposium on Theory of Computing, pages 462-467, 1992.
19. R. O'Donnell and R. Servedio. Learning monotone functions from random examples in polynomial time. Manuscript, 2005.
20. R. Rivest and J. Vuillemin. On recognizing graph properties from adjacency matrices. Theoretical Computer Science, 3:371-384, 1976.
21. L. Russo. On the critical percolation probabilities. Z. Wahrsch. werw. Gebiete, 43:39-48, 1978.
22. M. Saks and A. Wigderson. Probabilistic boolean decision trees and the complexity of evaluating game trees. In Proceedings of the 27th Annual Symposium on Foundations of Computer Science, pages 29-38, 1986.
23. O. Schramm and J. Steif. Quantitative noise sensitivity and exceptional times for percolation. Manuscript, 2005.
24. Y. Shi. Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of boolean variables. Information Processing Letters, 75(1-2):79-83, 2000.
25. M. Snir. Lower bounds for probabilistic linear decision trees. Theoretical Computer Science, 38:69-82, 1985.
26. J. M. Steele. An Efron-Stein inequality for nonsymmetric statistics. Annals of Statistics, (14):753-758, 1986.
27. M. Talagrand. On Russo's approximate 0-1 law. The Annals of Probability, 22(3):1576-1587, 1994.
28. A. Yao. Probabilistic computations: towards a unified measure of complexity. In Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS), pages 222-227, 1977.
29. A. Yao. Lower bounds to randomized algorithms for graph properties. In Proceedings of the 28th Annual Symposium on Foundations of Computer Science, pages 393-400, 1987.