Communication complexity

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

Dynamic multi-hop clustering for mobile hybrid wireless networks

Abstract: In mobile wireless networks communication is often improved by sending messages along a stable backbone of more reliable communication paths. Building such a backbone requires efficient clustering algorithms which aggregate network nodes into logical groups, each group being managed by a clusterhead and any two neighboring clusters being interconnected by at least one gateway node or gateway path. In this concept k-hop clustering refers to cluster structures where cluster members are at most k hops away from their clusterhead. While the dynamicity of mobile wireless network is often considered as a challenge, in this work we explicitly exploit node mobility in order to support cluster formation and maintenance of k-hop clusters. The described KHOPCA algorithm consists of a set of easy to implement rules which form and maintain k-hop sized clusters in a purely localized way. In a static network cluster formation is limited to a constant number of messages exchanges among neighboring nodes. In dynamic networks the localized nature of the described rules promise a fast cluster convergence and low communication complexity in case of mobility triggered cluster reconfiguration.

Separations in Query Complexity Based on Pointer Functions

Abstract: In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function f on n = 2k bits defined by a complete binary tree of NAND gates of depth k, which achieves R0(f) = O(D(f)0.7537…). We show that this is false by giving an example of a total Boolean function f on n bits whose deterministic query complexity is Ω(n) while its zero-error randomized query complexity is O(√ n). We further show that the quantum query complexity of the same function is O(n1/4), giving the first example of a total function with a super-quadratic gap between its quantum and deterministic query complexities.We also construct a total Boolean function g on n variables that has zero-error randomized query complexity Ω(n/ log (n)) and bounded-error randomized query complexity R(g) = O(√n). This is the first super-linear separation between these two complexity measures. The exact quantum query complexity of the same function is QE(g) = O(√n).These functions show that the relations D(f) = O(R1(f)2) and R0(f) = O(R(f)2) are optimal, up to polylogarithmic factors. Further variations of these functions give additional separations between other query complexity measures: a cubic separation between Q and R0, a 3/2-power separation between QE and R, and a 4th-power separation between approximate degree and bounded-error randomized query complexity.All of these examples are variants of a function recently introduced by Goos, Pitassi, and Watson, which they used to separate the unambiguous 1-certificate complexity from deterministic query complexity and to resolve the famous Clique versus Independent Set problem in communication complexity.

Interconnection framework for high-throughput, flexible LDPC decoders

Abstract: This paper presents a possible interconnection structure suitable for being used in a flexible LDPC decoder. The main feature of the proposed approach is the possibility of implementing parallel or semi-parallel decoders with a reduced communication complexity. To the best of our knowledge this is the first work detailing the implementation of a fully flexible LDPC decoder, able to support any type of code. To prove the effectiveness of this approach, a complete decoder has been implemented on a XC2V8000, achieving a decoding throughput of 529 Mbps on a (1920, 640) code.

Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition

Abstract: This paper makes three main contributions to the theory of communication complexity and stream computation. First, we present new bounds on the information complexity of augmented-index. In contrast to analogous results for index by Jain, Radhakrishnan, and Sen [J. ACM, 56 (2009), article 33], we have to overcome the significant technical challenge that protocols for augmented-index may violate the “rectangle property” due to the inherent input sharing. Second, we use these bounds to resolve an open problem of Magniez, Mathieu, and Nayak [Proceedings of the 42nd Annual ACM Symposium on Theory of Computing, 2010, pp. 261--270] that asked about the multipass complexity of recognizing Dyck languages. This results in a natural separation between the standard multipass model and the multipass model that permits reverse passes. Third, we present the first passive memory checkers that verify the interaction transcripts of priority queues, stacks, and double-ended queues. We obtain tight upper and lower bounds fo...

On Relay Assignment in Network-Coded Cooperative Systems

Abstract: We consider in this paper relay assignment for cooperative systems with multiple two-way relay channels. The nodes corresponding to one two-way relay channel (henceforth referred to as pair) communicate with each other through a relay. The relays use network coding to simultaneously transmit the signals corresponding to the pairs they are assigned to. We propose two relay assignment schemes. One scheme considers all possible relay assignment permutations and selects the one that yields the best performance, and the other one considers only a subset of these permutations and selects the best one. The advantage of the latter is that it results in a significant reduction in computational complexity, in addition to making the analysis more tractable. We analyze the performance of these schemes over asymmetric independent Rayleigh fading channels. We also consider semi-symmetric and symmetric channels as special cases. We derive closed-form expressions for the end-to-end bit error rate performance for all scenarios and show that the full diversity order is achieved, which is the number of available relays. We present several examples to verify the theoretical results.