TY - JOUR

T1 - Random sampling and approximation of MAX-CSP problems

AU - Alon, Noga

AU - De La Vega, W. Fernandez

AU - Kannan, Ravi

AU - Karpinski, Marek

PY - 2002

Y1 - 2002

N2 - We present a new efficient sampling method for approximating r-dimensional Maximum Constraint Satisfaction Problems, MAX-rCSP, on n variables up to an additive error εnr. We prove a new general paradigm in that it suffices, for a given set of constraints, to pick a small uniformly random subset of its variables, and the optimum value of the subsystem induced on these variables gives (after a direct normalization and with high probability) an approximation to the optimum of the whole system up to an additive error of εnr. Our method gives for the first time a polynomial in ε-1 bound on the sample size necessary to carry out the above approximation. Moreover, this bound is independent in the exponent on the dimension r. The above method gives a completely uniform sampling technique for all the MAX-rCSP problems, and improves the best known sample bounds for the low dimensional problems, like MAX-CUT. The method of solution depends on a new result on the cut norm of random subarrays, and a new sampling technique for high dimensional linear programs. This method could be also of independent interest.

AB - We present a new efficient sampling method for approximating r-dimensional Maximum Constraint Satisfaction Problems, MAX-rCSP, on n variables up to an additive error εnr. We prove a new general paradigm in that it suffices, for a given set of constraints, to pick a small uniformly random subset of its variables, and the optimum value of the subsystem induced on these variables gives (after a direct normalization and with high probability) an approximation to the optimum of the whole system up to an additive error of εnr. Our method gives for the first time a polynomial in ε-1 bound on the sample size necessary to carry out the above approximation. Moreover, this bound is independent in the exponent on the dimension r. The above method gives a completely uniform sampling technique for all the MAX-rCSP problems, and improves the best known sample bounds for the low dimensional problems, like MAX-CUT. The method of solution depends on a new result on the cut norm of random subarrays, and a new sampling technique for high dimensional linear programs. This method could be also of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=0036041771&partnerID=8YFLogxK

U2 - 10.1145/509943.509945

DO - 10.1145/509943.509945

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AN - SCOPUS:0036041771

SN - 0734-9025

SP - 232

EP - 239

JO - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

JF - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

T2 - Proceedings of the 34th Annual ACM Symposium on Theory of Computing

Y2 - 19 May 2002 through 21 May 2002

ER -