Explicit Interpolation Sets Using Perfect Hash Families

Let S be a set of functions with common domain D. We say X, a subset of D, an interpolation set for S if the values on X uniquely determine a function f in S. Recently, Piotr Indyk gave an explicit construction of interpolation sets of size O(k log n) for the family of boolean functions on n variables which depend symmetrically on at most k variables. Using perfect hash families, we have a variant of Indyk’s method to get an explicit construction of interpolation sets of size O(k logn log logn/ log log log n) for this family of functions.