The communication complexity of approximate set packing and covering

Abstract

We consider a setting where k players are each holdingsome collection of subsets of {1..n}. We consider the communication complexity of approximately solvingt wo problems: The cover number: the minimal number of sets (in the union of their collections) whose union is {1...n} and the packing number: the maximum number of sets (in the union of their collections) that are pair-wise disjoint. We prove that while computinga (ln n)-approximation for the cover number and an min(κ,O( √ n))-approximation for the packingn umber can be done with polynomial (in n) amount of communication, getting a (1/2 - ε) log n approximation for the cover number or a better than min(κ, n1/2-ε)-approximation for the packingn umber requires exponential communication complexity. © 2002 Springer-Verlag Berlin Heidelberg.