Abstract :
In this paper the communication complexity C(mn) of the cardinality of set intersection, mn say, will be determined up to one bit: n + ⌈log2(n + 1)⌉ − 1 ⩽ C(mn) ⩽ n + ⌈log2(n + 1)⌉.
The proof for the lower bound can also be applied to a larger class of “sum-type” functions sharing the property that f(0,y) = f(x,0) = 0 for all possible x,y. Furthermore, using Kraftʹs inequality for prefix codes, it is possible to find a communication protocol, which for n = 2t, t ⩾ 2, assumes the lower bound. The upper bound is assumed for n = 2t − 1, t ϵ N.
