Amortized communication complexity

The authors study the direct sum problem with respect to communication complexity: Consider a function f: D→{0, 1}, where D⊆{0, 1}ⁿ×{0, 1}ⁿ. The amortized communication complexity of f, i.e. the communication complexity of simultaneously computing f on l instances, divided by l is studied. The authors present, both in the deterministic and the randomized model, functions with communication complexity Θ(log n) and amortized communication complexity O(1). They also give a general lower bound on the amortized communication complexity of any function f in terms of its communication complexity C(f)