New Results in the Simultaneous Message Passing Model

Details New Results in the Simultaneous Message Passing Model New Results in the Simultaneous Message Passing Model

2009-02-18

arxiv.org/abs/0902.3056v1

Computer Science

Distributed, Parallel, and Cluster Computing

16 pages, version 1

Scientific paper

Consider the following Simultaneous Message Passing (SMP) model for computing a relation f subset of X x Y x Z. In this model Alice, on input x in X and Bob, on input y in Y, send one message each to a third party Referee who then outputs a z in Z such that (x,y,z) in 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, 2001, for the Equality function (and a class of other so-called robust functions), in the classical smp model with no shared resources between any parties. Furthermore we investigate the gap between the smp model and the one-way model in communication complexity and exhibit a partial function that is exponentially more expensive in the former if quantum communication with entanglement is allowed, compared to the latter even in the deterministic case.

Affiliated with

Also associated with

No associations

Rating

New Results in the Simultaneous Message Passing Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New Results in the Simultaneous Message Passing Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Results in the Simultaneous Message Passing Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127881