Communication complexity

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

On the power of quantum proofs

Abstract: We study the power of quantum proofs, or more precisely, the power of quantum Merlin-Arthur (QMA) protocols, in two well studied models of quantum computation: the black box model and the communication complexity model. Our main results are obtained for the communication complexity model. For this model, we identify a complete promise problem for QMA protocols, the linear sub-spaces distance problem. The problem is of geometrical nature: each player gets a linear subspace of R/sup m/ and considers the sphere of unit vectors in that subspace. Their goal is to output 1 if the distance between the two spheres is very small (say, smaller than 0.1 /spl middot/ /spl radic/2) and 0 if the distance is very large (say, larger than 0.9 /spl middot/ /spl radic/2). We show that: 1. The QMA communication complexity of the problem is O(logm). 2. The (classical) MA communication complexity of the problem is /spl Omega/(m/sup /spl epsi//) (for some /spl epsi/ > 0). 3. The (standard) quantum communication complexity of the problem is /spl Omega/(/spl radic/m). In particular, this gives an exponential separation between QMA communication complexity and MA communication complexity. For the black box model we give several observations. First, we observe that the block sensitivity method, as well as the polynomial method for proving lower bounds for the number of queries, can both be extended to QMA protocols. We use these methods to obtain lower bounds for the QMA black box complexity of functions. In particular, we obtain a tight lower bound of /spl Omega/(N) for the QMA black box complexity of a random function, and a tight lower bound of /spl Omega/(/spl radic/N) for the QMA black box query complexity of NOR(X/sub 1/,..., X/sub n/). In particular, this shows that any attempt to give short quantum proofs for the class of languages Co - NP have to go beyond black box arguments. We also observe that for any Boolean function G(X/sub 1/,..., X/sub n/), if for both G and 7minus;G there are QMA black box protocols that make at most T queries to the black box, then there is a classical deterministic black box protocol for G that makes 0(T/sup 6/) queries to the black box. In particular, this shows that in the black box model QMA /spl cap/ Co - QMA = P. On the positive side, we observe that any (total or partial) Boolean function G(X/sub 1/,..., X/sub n/) has a QMA black box protocol with proofs of length N that makes only 0(/spl radic/N) queries to the black box. Finally, we observe a very simple proof for the exponential separation (for promise problems) between QMA black box complexity and (classical) MA black box complexity (first obtained by Watrous).

Architectural Optimizations for Low-Power $K$ -Best MIMO Decoders

Abstract: Maximum-likelihood (ML) detection for higher order multiple-input-multiple-output (MIMO) systems faces a major challenge in computational complexity. This limits the practicality of these systems from an implementation point of view, particularly for mobile battery-operated devices. In this paper, we propose a modified approach for MIMO detection, which takes advantage of the quadratic-amplitude modulation (QAM) constellation structure to accelerate the detection procedure. This approach achieves low-power operation by extending the minimum number of paths and reducing the number of required computations for each path extension, which results in an order-of-magnitude reduction in computations in comparison with existing algorithms. This paper also describes the very-large-scale integration (VLSI) design of the low-power path metric computation unit. The approach is applied to a 4times4, 64-QAM MIMO detector system. Results show negligible performance degradation compared with conventional algorithms while reducing the complexity by more than 50%.

A dynamic Proof of Retrievability (PoR) scheme with O(logn) complexity

Abstract: Cloud storage has been gaining popularity because its elasticity and pay-as-you-go manner. However, this new type of storage model also brings security challenges. This paper studies the problem of ensuring data integrity in cloud storage. In the Proof of Retrievability (PoR) model, after outsourcing the preprocessed data to the server, the client will delete its local copies and only store a small amount of meta data. Later the client will ask the server to provide a proof that its data can be retrieved correctly. However, most of the prior PoR works apply only to static data. The existing dynamic version of PoR scheme has an efficiency problem. In this paper, we extend the static PoR scheme to dynamic scenario. That is, the client can perform update operations, e.g., insertion, deletion and modification. After each update, the client can still detect the data losses even if the server tries to hide them. We develop a new version of authenticated data structure based on a B+ tree and a merkle hash tree. We call it Cloud Merkle B+ tree (CMBT). By combining the CMBT with the BLS signature, we propose a dynamic version of PoR scheme. Compared with the existing dynamic PoR scheme, our worst case communication complexity is O(logn) instead of O(n).

Towards complexity metrics for Ada tasking

Abstract: Using Ada as a representative distributed programming language, the author discusses some ideas on complexity metrics that focus on Ada tasking and rendezvous. Concurrently active rendezvous are claimed to be an important aspect of communication complexity. A Petri net graph model of Ada rendezvous is used to introduce a rendezvous graph, an abstraction that can be useful in viewing and computing effective communication complexity. >

On the "log rank"-conjecture in communication complexity

Abstract: We show the existence of a non-constant gap between the communication complexity of a function and the logarithm of the rank of its input matrix. We consider the following problem: each of two players gets a perfect matching between two n-element sets of vertices. Their goal is to decide whether or not the union of the two matchings forms a Hamiltonian cycle. We prove: (1) The rank of the input matrix over the reals for this problem is 2/sup O(n)/. (2) The non-deterministic communication complexity of the problem is /spl Omega/(n log log n). Our result also supplies a superpolynomial gap between the chromatic number of a graph and the rank of its adjacency matrix. Another conclusion from the second result is an /spl Omega/(n log log n). Lower bound for the graph connectivity problem in the non-deterministic case. We make use of the theory of group representations for the first result. The second result is proved by an information theoretic argument. >