Communication complexity

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

Implementation Aspects of List Sphere Detector Algorithms

Abstract: A list sphere detector (LSD) can be used to approximate the optimal maximum a posteriori (MAP) detection. The total complexity of the LSD algorithms is relative to the number of visited nodes in the search tree. We compare the differences between real and complex signal model in the LSD algorithm implementation and study its impact on the complexity and performance with different search strategies. In hardware implementation, the number of visited nodes needs to be bounded in order to determine the complexity and the latency of the implementation. Thus, we study the performance of LSD algorithms with a limited number of nodes in the search. We show that the algorithms with real signal model are less complex compared to the complex signal model, and that the performance may suffer significantly with limited search depending on the search strategy.

Decentralized Cooperative Localization for Heterogeneous Multi-robot System Using Split Covariance Intersection Filter

Abstract: This study proposes the use of a split covariance intersection filter (Split-CIF) for decentralized multi-robot cooperative localization. In the proposed method each robot maintains a local extended Kalman filter to estimate its own pose in a pre-defined reference frame. When a robot receives pose information from neighbouring robots it employs a Split-CIF-based approach to fuse this received measurement with its local belief. For a team of N mobile robots, the processing and communication complexity of the proposed method is linear, O(N), with respect to the number of robots in the team. The proposed method does not demand for fully connected synchronous communication channels between robots and can work with any asynchronous and partially connected communication network. Additionally, the proposed method gives consistent state updates and is capable of handling independent and interdependent parts of the estimations separately. The numerical simulations presented validate the proposed algorithm. The simulation results demonstrate that the proposed algorithm is outperformed compared to single-robot localization algorithms and also demonstrate approximately the same estimation accuracy as a centralized cooperative localization approach but with reduced computational cost.

On the Space and Access Complexity of Computation DAGs

Abstract: We study the space and the access complexity of computations represented by Computational Directed Acyclic Graphs (CDAGs) in hierarchical memory systems. First, we present a unifying framework for proving lower bounds on the space complexity, which captures most of the bounds known in the literature for relevant CDAGs, previously proved through ad-hoc arguments. Then, we expose a close relationship between the notions of space and access complexity, where the latter represents the minimum number of accesses performed by any computation of a CDAG at a given level of the memory hierarchy. Specifically, we present two general techniques to derive bounds on the access complexity of a CDAG based on the space complexity of certain subgraphs. One technique, simpler to apply, provides only lower bounds, while the other provides (almost) matching lower and upper bounds and improves upon previous well-known result by Hong and Kung.

Amortized complexity of information-theoretically secure MPC revisited

Abstract: A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general n-player MPC shows how one may trade the adversary threshold t against amortized communication complexity, by using a so-called packed version of Shamir’s scheme. For e.g. the BGW-protocol (with active security), this trade-off means that if \(t + 2k -2 < n/3\), then k parallel evaluations of the same arithmetic circuit on different inputs can be performed at the overall cost corresponding to a single BGW-execution.