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Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.


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TL;DR: The main known lower bounds on the minimum sizes of extended formulations for fixed polytope P (Yannakakis 1991) are closely related to the concept of non-deterministic communication complexity as mentioned in this paper.
Abstract: An extended formulation of a polytope P is a polytope Q which can be projected onto P. Extended formulations of small size (i.e., number of facets) are of interest, as they allow to model corresponding optimization problems as linear programs of small sizes. The main known lower bounds on the minimum sizes of extended formulations for fixed polytope P (Yannakakis 1991) are closely related to the concept of nondeterministic communication complexity. We study the relative power and limitations of the bounds on several examples.

82 citations

Proceedings ArticleDOI
06 Jul 2001
TL;DR: It is shown that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k quantum communication complexity, thus answering the question as to whether every classical protocol may be transformed to a “simpler” quantum protocol in the negative.
Abstract: One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with exponentially fewer qubits than possible classically [3, 26]. Moreover, these methods have a very simple structure---they involve only few message exchanges between the communicating parties.We consider the question as to whether every classical protocol may be transformed to a “simpler” quantum protocol---one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the above question in the negative. This in particular proves a round hierarchy theorem for quantum communication complexity, and implies via a simple reduction, an \Omega(N^{1/k}) lower bound for k message protocols for Set Disjointness for constant~k.Our result builds on two primitives, local transitions in bi-partite states (based on previous work) and average encoding which may be of significance in other contexts as well.

81 citations

Proceedings ArticleDOI
09 Jun 2013
TL;DR: A coalitional game with transferable utility, in which each user intends to maximize its own utility and has the incentive to cooperate with other users to form a strengthened user group that can increase the opportunity to win its preferred spectrum resources.
Abstract: In this paper, we investigate the resource sharing problem to optimize the system performance in device-to-device (D2D) communications underlaying cellular networks from a distributed and cooperative perspective. Specifically, we formulate a coalitional game with transferable utility, in which each user intends to maximize its own utility and has the incentive to cooperate with other users to form a strengthened user group that can increase the opportunity to win its preferred spectrum resources. Furthermore, we propose a distributed merge-and-split based coalition formation algorithm based on a new defined Max-Coalition order to effectively process the resource allocation problem. Simulation results confirm that, with much lower computational complexity, the proposed scheme achieves an approaching performance in terms of network sum-rate compared with the centralized optimal resource allocation scheme obtained via exhaustive search.

81 citations

Journal ArticleDOI
TL;DR: This paper studies the SIMULTANEOUS MESSAGES (SM) model of multiparty communication complexity, a restricted version of the CFL game in which the players are not allowed to communicate with each other, and proves lower and upper bounds on the SM complexity of several classes of explicit functions.
Abstract: In the multiparty communication game (CFL game) of Chandra, Furst, and Lipton [Proceedings of the 15th Annual ACM Symposium on Theory of Computing, Boston, MA, 1983, pp. 94--99] k players collaboratively evaluate a function f(x0, . . . , xk-1) in which player i knows all inputs except xi. The players have unlimited computational power. The objective is to minimize communication. In this paper, we study the SIMULTANEOUS MESSAGES (SM) model of multiparty communication complexity. The SM model is a restricted version of the CFL game in which the players are not allowed to communicate with each other. Instead, each of the k players simultaneously sends a message to a referee, who sees none of the inputs. The referee then announces the function value. We prove lower and upper bounds on the SM complexity of several classes of explicit functions. Our lower bounds extend to randomized SM complexity via an entropy argument. A lemma establishing a tradeoff between average Hamming distance and range size for transformations of the Boolean cube might be of independent interest. Our lower bounds on SM complexity imply an exponential gap between the SM model and the CFL model for up to $(\log n)^{1-\epsilon}$ players for any $\epsilon > 0$. This separation is obtained by comparing the respective complexities of the Generalized Addressing Function, GAFG,k, where G is a group of order n. We also combine our lower bounds on SM complexity with the ideas of Hastad and Goldmann [Comput. Complexity, 1 (1991), pp. 113--129] to derive superpolynomial lower bounds for certain depth-2 circuits computing a function related to the GAF function. We prove some counterintuitive upper bounds on SM complexity. We show that {\sf GAF}$_{\mathbb{Z}_2^t,3}$ has SM complexity $O(n^{0.92})$. When the number of players is at least $c\log n$, for some constant c>0, our SM protocol for {\sf GAF}$_{\mathbb{Z}_2^t,k}$ has polylog(n) complexity. We also examine a class of functions defined by certain depth-2 circuits. This class includes the Generalized Inner Product function and Majority of Majorities. When the number of players is at least 2+log n, we obtain polylog(n) upper bounds for this class of functions.

81 citations

Proceedings ArticleDOI
17 Oct 2015
TL;DR: It is shown that deterministic communication complexity can be super logarithmic in the partition number of the associated communication matrix and near-optimal deterministic lower bounds for the Clique vs. Independent Set problem are obtained.
Abstract: We show that deterministic communication complexity can be super logarithmic in the partition number of the associated communication matrix. We also obtain near-optimal deterministic lower bounds for the Clique vs. Independent Set problem, which in particular yields new lower bounds for the log-rank conjecture. All these results follow from a simple adaptation of a communication-to-query simulation theorem of Raz and McKenzie (Combinatorica 1999) together with lower bounds for the analogous query complexity questions.

81 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202256
2021161
2020165
2019149
2018141