Approximating multilinear monomial coefficients and maximum multilinear monomials in multivariate polynomials

Journal of Combinatorial Optimization

Volumn 25, Issue 2, 2013, Pages 234-254

  Chen, Zhixiang ^a   Fu, Bin ^a  

^a UNIVERSITY OF TEXAS PAN AMERICAN   (United States)

Author keywords

Approximation algorithms; Inapproximability; Maximum multilinear monomials; Monomial coefficient computing; Monomial testing; Multivariate polynomials

Indexed keywords

APPROXIMATION ALGORITHMS; COMBINATORIAL OPTIMIZATION; COMPUTATION THEORY; MULTIVARIABLE SYSTEMS;

APPROXIMATION FACTOR; ARITHMETIC CIRCUIT; INAPPROXIMABILITY; MAXIMUM MULTILINEAR MONOMIALS; MONOMIAL COEFFICIENT COMPUTING; MULTIVARIATE POLYNOMIAL; RANDOMIZED APPROXIMATION SCHEMES; UNIQUE GAMES CONJECTURE;

POLYNOMIAL APPROXIMATION;

EID: 84879554772     PISSN: 13826905     EISSN: 15732886     Source Type: Journal    
DOI: 10.1007/s10878-012-9496-5     Document Type: Article

References (28)

1. Agrawal M, Biswas S (2003) Primality and identity testing via Chinese remaindering. J ACM 50(4):429-443
2. Agrawal M, Kayal N, Saxena N (2004) PRIMES is in P. Ann Math 160(2):781-793
3. Arora S, Lund C, Motwani R, Sudan M, Szegedy M (1998) Proof verification and the hardness of approximation problems. J ACM 45(3):501-555
4. Beigel R (1993) The polynomial method in circuit complexity. In: Proceedings of the eighth conference on structure in complexity theory, pp 82-95
5. N -DNF formulas. In: Proceedings of the eighth annual conference on computational learning theory, COLT 1995, Santa Cruz, California, USA. ACM, New York, 1995, pp 198-205
6. Chen Z, Fu B (2010) Approximating multilinear monomial coefficients and maximum multilinear monomials in multilinear polynomials (extended abstract). In: Proceedings of the fourth international conference on combinatorial optimization and applications, COCOA 2010. Lecture notes in computer science, vol 6508, pp 309-323
7. Chen Z, Fu B (2011) The complexity of testing monomials in multivariate polynomials. In: Proceedings of the fourth international conference on combinatorial optimization and applications, COCOA 2011, August 2011. Lecture notes in computer science, vol 6831, pp 1-15
8. Chen Z-Z, Kao M-Y (2000) Reducing randomness via irrational numbers. SIAM J Comput 29(4):1247-1256
9. Chen Z, Fu B, Zhu B (2006) The approximability of the exemplar breakpoint distance problem. In: Proceedings of the second annual international conference on algorithmic aspects in information and management (AAIM). Lecture notes in computer science, vol 4041. Springer, Berlin, pp 291-302
10. Chen J, Lu S, Sze S-H, Zhang F (2007) Improved algorithms for path, matching, and packing problems. In: SODA, pp 298-307
11. Chen Z, Fowler RH, Fu B, Zhu B (2008) On the inapproximability of the exemplar conserved interval distance problem of genomes. J Comb Optim 15(2):201-221
12. Chen Z, Fu B, Liu Y, Schweller R (2011) Algorithms for testing monomials in multivariate polynomials. In: Proceedings of the fifth international conference on combinatorial optimization and applications, COCOA 2011. Lecture notes in computer science, vol 6831, pp 16-30
13. Chen Z, Fu B, Liu Y, Schweller R (2012) On testing monomials in multivariate polynomials. Theor Comput Sci. doi: 10.1016/j.tcs.2012.03.038
14. Feige U, Goldwasser S, Lovász L, Safra S, Szegedy M (1996) Interactive proofs and the hardness of approximating cliques. J ACM 43(2):268-292
15. Fu B (1992) Separating PH from PP by relativization. Acta Math Sin 8(3):329-336
16. Hästad J (2001) Some optimal inapproximability results. J ACM 48(4):798-859
17. Jerrum M, Sinclaire A, Vigoda E (2004) A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries. J ACM 51(4):671-697
18. Kabanets V, Impagliazzo R (2003) Derandomizing polynomial identity tests means proving circuit lower bounds. In: STOC, pp 355-364
19. Khot S, Kindler G, Mossel E, O'Donnell R (2004) Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? In: Proceedings of the 45th annual IEEE symposium on foundations of computer science, FOCS'04, pp 146-154
20. Klivans A, Servedio RA (2001) Learning DNF in time. In: STOC, pp 258-265
21. Koutis I (2008) Faster algebraic algorithms for path and packing problems. In: Proceedings of the international colloquium on automata, language and programming, ICALP. Lecture notes in computer science, vol 5125. Springer, Berlin, pp 575-586
22. Minsky M, Papert S (1968) Perceptrons. MIT Press, Cambridge (expanded edition 1988)
23. Raz R, Shpilka A (2005) Deterministic polynomial identity testing in non-commutative models. Comput Complex 14(1):1-19
24. Ryser HJ (1963) Combinatorial mathematics. Carus mathematical monographs, vol 14. Math. Assoc. of America, Washington
25. Shamir A (1992) IP = PSPACE. J ACM 39(4):869-877
26. Valiant LG (1979) The complexity of computing the permanent. Theor Comput Sci 8(2):189-201
27. k ) time. Inf Process Lett 109:315-318
28. Zuckerman D (2007) Linear degree extractors and the inapproximability of max clique and chromatic number. Theory Comput 3:103-128