1/1/1973 · A collection F of sets is k-independent if for any selections A, B of k 1 and k 2 of its members with k 1 +k 2 =k, there are elements in all the members of A and not in the members of B.Bounds on the maximal size of k-independent families exponential in the total number of elements are obtained.
DJ. Kicihnan, J. Spencer, Families of k-independent setr Theorem 4. If F is a k-independent family of subsets of S, I S 1= n, and G is a collection of m nonsddisjoint subsets which span S n (Ail n Ai2 . nAit) with A’,, E F * fiw each p, and t + m < k, then some member of G is not x.7 rained %n any mem bclr of [F* - {A i, . , AiP )] Mere F * consists of, In computer science, a family of hash functions is said to be k-independent or k-universal if selecting a function at random from the family guarantees that the hash codes of any designated k keys are independent random variables. Such families allow good average case performance in randomized algorithms or data structures, even if the input data is chosen by an adversary. The trade-offs.Explicit construction of exponential sized families of k-independent sets 193 (2) We made no attempt to maximize the value of Ck given in (2.1) in our basic construction. One can easily improve (2.1) by a slightly more careful construc- tion, but even the improved bound will be, of …
