论文信息 - Kernelization, Constraint Satisfaction Problems Parameterized above Average

Kernelization, Constraint Satisfaction Problems Parameterized above Average

Let r be an integer, let V D fv1; : : : ; vng be a set of variables, each taking values 1 (TRUE) and 1 (FALSE), and let be a set of Boolean functions, each involving at most r variables from V . In the problem MAX-r-CSP, we are given a collection F of m Boolean functions, each f 2 F being a member of and each with a positive integral weight. Our aim is to find a truth assignment that maximizes the total weight of satisfied functions from F . We will denote the maximum by sat.F/: Let A be the average weight (over all truth assignments) of satisfied functions. Observe that A is a lower bound for sat.F/: In fact, A is a tight lower bound, whenever the family is closed under replacing each variable by its complement [1]. Thus, it is natural to parameterize MAX-r-CSP as follows (AA stands for Above Average).

Gregory Gutin

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