On testing convexity and submodularity

SIAM Journal on Computing

Volumn 32, Issue 5, 2003, Pages 1158-1184

  Parnas, Michal ^a   Ron, Dana ^b   Rubinfeld, Ronitt ^c  

^a ACADEMIC COLLEGE OF TEL AVIV YAFFO   (Israel)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEC LABORATORIES AMERICA   (United States)

Author keywords

Approximation algorithms; Convex functions; Monge matrices; Property testing; Randomized algorithms

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; GAME THEORY; MATRIX ALGEBRA; OPTIMIZATION; PROBABILITY; PROBLEM SOLVING;

MONGE MATRICES; PROPERTY TESTING; RANDOMIZED ALGORITHMS;

FUNCTION EVALUATION;

EID: 0344153348     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539702414026     Document Type: Article

References (15)

1. R. E. Burkard, B. Klinz, and R. Rudolf, Perspectives of Monge properties in optimization, Discrete Appl. Math., 70 (1996), pp. 95-161.
2. T. Batu, R. Rubinfeld, and P. White, Fast approximate PCPs for multidimensional bin-packing problems, in Proceedings of Random, Berkeley, CA, 1999, pp. 245-256.
3. Y. Dodis, O. Goldreich, E. Lehman, S. Raskhodnikova, D. Ron, and A. Samorodnitsky, Improved testing algorithms for monotonocity, in Proceedings of Random, Berkeley, CA, 1999, pp. 97-108.
4. S. de Vries and R. Vohra, Combinatorial Auctions: A Survey, http://www.kellogg.nwu.edu/faculty/vohra/htm/res.htm (2000).
5. F. Ergun, S. Kannan, S. R. Kumar, R. Rubinfeld, and M. Viswanathan, Spotcheckers, J. Comput. System Sci., 60 (2000), pp. 717-751.
6. E. Fischer, The art of uninformed decisions: A primer to property testing, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS, 75 (2001), pp. 97-126.
7. O. Goldreich, S. Goldwasser, and D. Ron, Property testing and its connection to learning and approximation, J. ACM, 45 (1998), pp. 653-750.
8. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), pp. 169-197.
9. A. J. Hoffman, On Simple Linear Programming Problems, Proc. Sympos. Pure Math. 7, AMS, Providence, RI, 1963, pp. 317-327.
10. S. Iwata, L. Fleischer, and S. Fujishige, A combinatorial strongly polynomial algorithm for minimizing submodular functions, J. ACM, 48 (2001), pp. 761-777.
11. B. Lehmann, D. Lehmann, and N. Nisan, Combinatorial auctions with decreasing marginal utilities, in Proceedings of the ACM Conference on Electronic Commerce, Tampa, FL, 2001.
12. L. Lovász, Submodular functions and convexity, Mathematical Programming: The State of the Art, 1983, Springer, Berlin, pp. 235-257.
13. D. Ron, Property testing, in Handbook on Randomization, Vol. II, S. Rajasekaran, P. Pardalos, J. Reif, and J. Rolim, eds., Kluwer Academic Publishers, Dordrecht, 2001, pp. 597-649.
14. R. Rubinfeld and M. Sudan, Robust characterization of polynomials with applications to program testing, SIAM J. Comput., 25 (1996), pp. 252-271.
15. A. Schrijver, A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combin. Theory Ser. B, 80 (2000), pp. 346-355.