300 research outputs found
Tight Bounds for Set Disjointness in the Message Passing Model
In a multiparty message-passing model of communication, there are
players. Each player has a private input, and they communicate by sending
messages to one another over private channels. While this model has been used
extensively in distributed computing and in multiparty computation, lower
bounds on communication complexity in this model and related models have been
somewhat scarce. In recent work \cite{phillips12,woodruff12,woodruff13}, strong
lower bounds of the form were obtained for several
functions in the message-passing model; however, a lower bound on the classical
Set Disjointness problem remained elusive.
In this paper, we prove tight lower bounds of the form
for the Set Disjointness problem in the message passing model. Our bounds are
obtained by developing information complexity tools in the message-passing
model, and then proving an information complexity lower bound for Set
Disjointness. As a corollary, we show a tight lower bound for the task
allocation problem \cite{DruckerKuhnOshman} via a reduction from Set
Disjointness
A Lower Bound for Sampling Disjoint Sets
Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x subseteq[n] and Bob ends up with a set y subseteq[n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant beta0 of the uniform distribution over all pairs of disjoint sets of size sqrt{n}
Separating NOF communication complexity classes RP and NP
We provide a non-explicit separation of the number-on-forehead communication
complexity classes RP and NP when the number of players is up to \delta log(n)
for any \delta<1. Recent lower bounds on Set-Disjointness [LS08,CA08] provide
an explicit separation between these classes when the number of players is only
up to o(loglog(n))
Tribes Is Hard in the Message Passing Model
We consider the point-to-point message passing model of communication in
which there are processors with individual private inputs, each -bit
long. Each processor is located at the node of an underlying undirected graph
and has access to private random coins. An edge of the graph is a private
channel of communication between its endpoints. The processors have to compute
a given function of all their inputs by communicating along these channels.
While this model has been widely used in distributed computing, strong lower
bounds on the amount of communication needed to compute simple functions have
just begun to appear. In this work, we prove a tight lower bound of
on the communication needed for computing the Tribes function,
when the underlying graph is a star of nodes that has leaves with
inputs and a center with no input. Lower bound on this topology easily implies
comparable bounds for others. Our lower bounds are obtained by building upon
the recent information theoretic techniques of Braverman et.al (FOCS'13) and
combining it with the earlier work of Jayram, Kumar and Sivakumar (STOC'03).
This approach yields information complexity bounds that is of independent
interest
Bounds on oblivious multiparty quantum communication complexity
The main conceptual contribution of this paper is investigating quantum
multiparty communication complexity in the setting where communication is
\emph{oblivious}. This requirement, which to our knowledge is satisfied by all
quantum multiparty protocols in the literature, means that the communication
pattern, and in particular the amount of communication exchanged between each
pair of players at each round is fixed \emph{independently of the input} before
the execution of the protocol. We show, for a wide class of functions, how to
prove strong lower bounds on their oblivious quantum -party communication
complexity using lower bounds on their \emph{two-party} communication
complexity. We apply this technique to prove tight lower bounds for all
symmetric functions with \textsf{AND} gadget, and in particular obtain an
optimal lower bound on the oblivious quantum -party
communication complexity of the -bit Set-Disjointness function. We also show
the tightness of these lower bounds by giving (nearly) matching upper bounds.Comment: 13 pages, an accepted paper of LATIN 202
Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness
We show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Omega(n/4^k). This gives the first lower bound that is linear in n, nearly matching Grolmusz\u27s upper bound of O(log^2(n) + k^2n/2^k). We also simplify the proof of Sherstov\u27s Omega(sqrt(n)/(k2^k)) lower bound for the randomized communication complexity of set disjointness
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