Questions tagged [communication-complexity]

Questions regarding the amount of communication needed to accomplish a computational task, when the information about the task is spread across several agents

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11
votes
3answers
305 views

Bounds on approximating frequency moments

Let $a_1, a_2,\dotsc, a_m$ be a sequence of integers where each $a_j \in \{1,2,\dotsc,n\}$. For $i \in \{1,2,\dotsc,n\}$, let $m_i = |\{j : a_j = i\}|$. The $k$th frequency moment is defined to be $\...
9
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2answers
562 views

Communication complexity with a referee

Assume a framework in communication complexity where we have two players A(lice) and B(ob) and a R(eferee). A and B don't communicate directly with each other. In each round of communication, each of ...
17
votes
0answers
351 views

Descriptive complexity of communication complexity classes

It is well known that some major complexity classes, like P or NP, admit a full logical characterization (e.g NP = existential 2nd order logic by Fagin's theorem). On the other hand, one can also ...
11
votes
2answers
552 views

Nonlocal Games and Quantum Communication

I'm currently on the look out for some good reference material relating non-local games with beneficial aspects in quantum communication. For instance, I am aware that non-local games are good at ...
7
votes
1answer
94 views

Effect of protocol ordering on multiparty comm. complexity

Brief Background In Multi-Party Protocols by Chandra, Lipton, and Furst [CFL83], a Ramsey-theoretic proof is used to show a lower bound (and later, a matching upper bound) for the predicate Exactly-$...
4
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1answer
585 views

Monochromatic Rectangle Tiling

This problem originates from the tiling lowerbound method for communication complexity. In that method, there is a 0-1 matrix $M_{n \times n}$. A rectangle is defined as a submatrix $A \times B$ where ...
6
votes
1answer
617 views

Existence of zero-knowledge proof for location

N items have been placed at specific points on a map. A prize is awarded to the first person who turns in a list with the location of all N items. The location of each item must fall with a distance ...
10
votes
1answer
359 views

What is the largest gap between rank and approximate rank?

We know that the log of the rank of a 0-1 matrix is the lower bound of deterministic communication complexity, and the log of the approximate rank is the lower bound of randomized communication ...
4
votes
1answer
253 views

Why does deterministic recognition of DYCK(2) languages in the streaming model take linear space?

I was reading the paper "Recognizing Well-Paranthesized Expressions in the Streaming Model" by Magniez, Mathieu and Nayak where they give upper and lower bounds on the space required to recognize DYCK(...
12
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2answers
677 views

Best alien communication protocol?

Let's say we discover alien civilizations that are able to send and receive messages using an interstellar digital communications channel. (Say using modulated radio waves, laser pulses, re-...
8
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2answers
358 views

Finding out a set by intersection comparison

The following problem recently emerged from my research and I would like to ask if anyone knows if this problem was considered before or has heard of anything that might be related. The general ...
8
votes
3answers
790 views

One way randomised communication complexity of disjointness

I am looking for a reference for the (classical) one way randomised communication complexity of disjointness when the universe can be large. Say Alice and Bob both have sets of size $m$ chosen from a ...
22
votes
2answers
1k views

Protocol partition number and deterministic communication complexity

Besides (deterministic) communication complexity $cc(R)$ of a relation $R$, another basic measure for the amount of communication needed is the protocol partition number $pp(R)$. The relation between ...
20
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4answers
1k views

Communication Complexity …Classes?

Discussion: I've been spending some personal time lately learning various things in communication complexity. For instance, I've re-familiarized myself with the relevant chapter in Arora/Barak, ...
6
votes
1answer
358 views

Stronger Lower Bounds on Nondeterministic Multiparty Communication

This is a continuation of my previous question on Lower bounds for Nondeterministic Multiparty Communication. From the answer, the $\mu^\infty$ norm lower bounds nondeterministic multiparty ...
11
votes
1answer
462 views

Lower bounds for Nondeterministic Multiparty Communication

This is a continuation of my previous question on communication lower bounds for partial boolean functions. Can someone suggest any reference on lower bounds for nondeterministic multiparty ...
7
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2answers
626 views

Communication lower bounds for partial boolean functions

There are well known techniques for proving lower bounds on the communication complexity of boolean functions, like fooling sets, the rank of the communication matrix, and discepancy. 1) How do we ...
13
votes
2answers
441 views

multi-party Communication complexity of “Set Partition problem”

In an application I'm considering, I need to know the communication complexity of the following problem: Given $n$, let $S$ be the set of integers from $1$ to $n$. Alice, Bob, and Carol each ...
12
votes
1answer
750 views

Communication complexity for deciding associativity

Let $S=${$0,...,n-1$} and $\circ : S \times S \rightarrow S$. I want to compute the communication complexity of deciding whether $\circ$ is associative. The model is the following. $\circ$ is given ...
25
votes
2answers
983 views

Approximating the sign rank of a matrix

The sign rank of a matrix A with +1,-1 entries is the least rank (over the reals) of a matrix B which has the same sign pattern as A (i.e., $A_{ij}B_{ij}>0$ for all $i,j$). This notion is important in ...

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