New strong direct product results in communication complexity

We show two new direct product results in two different models of communication complexity. Our first result is in the model of one-way public-coin model. Let f ⊆ X × Y × Z be a relation and ε > 0 be a constant. Let R1,pub ε (f) represent the communication complexity of f, with worst case error ε in this model. We show that if for computing fk (k independent copies of f) in this model, o(k · R1,pub 1/3 (f)) communication is provided, then the success is exponentially small in k. To our knowledge this is the first time a strong direct product result holding for all relations has been shown in any model of communication complexity. We show a new tight characterization of communication complexity in this model which strengthens on the tight characterization shown in J., Klauck, Nayak [JKN08]. We use this new characterization to show our direct product result and this characterization may also be of independent interest. Our second direct product result is in the model of tw...

• Type: Journal
• Year: 2011
• Where: ECCC
• Authors: Rahul Jain
• Keywords: Communication Complexity, ECCC 2011, ECommerce, Model, Strong Direct Product