New Results in the Simultaneous Message Passing Model via Information Theoretic Techniques

—Consider the following Simultaneous Message Passing (SMP) model for computing a relation f ⊆ X ×Y ×Z. In this model Alice, on input x ∈ X and Bob, on input y ∈ Y, send one message each to a third party Referee who then outputs a z ∈ Z such that (x, y, z) ∈ f. We first show optimal Direct sum results for all relations f in this model, both in the quantum and classical settings, in the situation where we allow shared resources (shared entanglement in quantum protocols and public coins in classical protocols) between Alice and Referee and Bob and Referee and no shared resource between Alice and Bob. This implies that, in this model, the communication required to compute k simultaneous instances of f, with constant success overall, is at least k-times the communication required to compute one instance with constant success. This in particular implies an earlier Direct sum result, shown by Chakrabarti, Shi, Wirth and Yao [CSWY01] for the Equality function (and a class of oth...

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Rahul Jain, Hartmut Klauck
• Keywords: COCO 2009, Model, Shared Resources, Simultaneous Message, Theoretical Computer Science