Maximization of Approximately Submodular Functions
نویسندگان
چکیده
We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that F is ε-approximately submodular if there exists a submodular function f such that (1−ε)f(S) ≤ F (S) ≤ (1+ε)f(S) for all subsets S. We are interested in characterizing the query-complexity of maximizing F subject to a cardinality constraint k as a function of the error level ε > 0. We provide both lower and upper bounds: for ε > n−1/2 we show an exponential query-complexity lower bound. In contrast, when ε < 1/k or under a stronger bounded curvature assumption, we give constant approximation algorithms.
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