Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.

A Very Low Complexity QRD-M Algorithm Based on Limited Tree Search for MIMO Systems

Abstract: We present a very low complexity QRD-M algorithm for MIMO systems. The original QRD-M algorithm decomposes the MIMO channel matrix into upper triangular matrix and applies a limited tree search. To accomplish near- MLD(Maximum Likelihood Detection) performance for QRD-M algorithm, number of search points at each layer must be the modulation size. In the proposed scheme, each of survival branches are extended only to the corresponding QR decomposition (QRD)-based detection symbol in the next layer and its neighboring symbols in the constellation. Using this approach, we can significantly decrease the complexity of conventional QRD-M algorithm. Simulation results show that the proposed algorithm scheme achieves the detection performance near to that of the MLD with negligibly low complexity.

A direct product theorem

Abstract: Gives a general setting in which the complexity (or quality) of solving two independent problems is the product of the associated individual complexities. The authors then derive from this setting several concrete results of this type for decision trees and communication complexity. >

The complexity of plan existence and evaluation in robabilistic domains

Abstract: We examine the computational complexity of testing and finding small plans in probabilistic planning domains with succinct representations. We find that many problems of interest are complete for a variety of complexity classes: NP, co-NP, PP, NPPP, co-NP PP, and PSPACE. Of these, the probabilistic classes PP and NPPP are likely to be of special interest in the field of uncertainty in artificial intelligence and are deserving of additional study. These results suggest a fruitful direction of future algorithmic development.

Space and Time Complexity of Exact Algorithms: Some Open Problems (Invited Talk).

Abstract: We discuss open questions around worst case time and space bounds for NP-hard problems. We are interested in exponential time solutions for these problems with a relatively good worst case behavior.

Parameterized Computation and Complexity: A New Approach Dealing with NP-Hardness

Abstract: The theory of parameterized computation and complexity is a recently developed subarea in theoretical computer science. The theory is aimed at practically solving a large number of computational problems that are theoretically intractable. The theory is based on the observation that many intractable computational problems in practice are associated with a parameter that varies within a small or moderate range. Therefore, by taking the advantages of the small parameters, many theoretically intractable problems can be solved effectively and practically. On the other hand, the theory of parameterized computation and complexity has also offered powerful techniques that enable us to derive strong computational lower bounds for many computational problems, thus explaining why certain theoretically tractable problems cannot be solved effectively and practically. The theory of parameterized computation and complexity has found wide applications in areas such as database systems, programming languages, networks, VLSI design, parallel and distributed computing, computational biology, and robotics. This survey gives an overview on the fundamentals, algorithms, techniques, and applications developed in the research of parameterized computation and complexity. We will also report the most recent advances and excitements, and discuss further research directions in the area.