Private approximation of NP-hard functions

d Abstract] Shai Halevi Robert Krauthgamer Eyal Kushilevitz Kobbi Nissim ? The notion of private approximation was introduced recently by Feigenbaum, Fong, Strauss and Wright. Informally, a private approximation of a function f is another function F that approximates f in the usual sense, but does not yield any information on x other than what can be deduced from f(x). As such, F(x) is useful for private computation of f(x) (assuming that F can be computed more efficiently than f). In this work we examine the properties and limitations of this new notion. Specifically, we show that for many NP-hard problems, the privacy requirement precludes nontrivial approximation. This is the case even for problems that otherwise admit very good approximation (e.g., problems with PTAS). On the other hand, we show that slightly relaxing the privacy requirement, by means of leaking "just a few bits of information" about x, again permits good approximation.

• Type: Conference
• Year: 2001
• Where: STOC
• Authors: Shai Halevi, Robert Krauthgamer, Eyal Kushilevitz, Kobbi Nissim
• Keywords: Algorithms, Nontrivial Approximation, Privacy Requirement, Private Approximation, STOC 2001