Search results for "Worst-case complexity"
showing 8 items of 8 documents
An Introduction to Computational Complexity
2016
This chapter is not strictly about algebra. However, this chapter offers a set of mathematical and computational instruments that will allow us to introduce several concepts in the following chapters. Moreover, the contents of this chapter are related to algebra as they are ancillary concepts that help (and in some cases allow) the understanding of algebra.
Non-intersecting Complexity
2006
A new complexity measure for Boolean functions is introduced in this article. It has a link to the query algorithms: it stands between both polynomial degree and non-deterministic complexity on one hand and still is a lower bound for deterministic complexity. Some inequalities and counterexamples are presented and usage in symmetrisation polynomials is considered.
Reducing complexity in H.264/AVC motion estimation by using a GPU
2011
H.264/AVC applies a complex mode decision technique that has high computational complexity in order to reduce the temporal redundancies of video sequences. Several algorithms have been proposed in the literature in recent years with the aim of accelerating this part of the encoding process. Recently, with the emergence of many-core processors or accelerators, a new approach can be adopted for reducing the complexity of the H.264/AVC encoding algorithm. This paper focuses on reducing the inter prediction complexity adopted in H.264/AVC and proposes a GPU-based implementation using CUDA. Experimental results show that the proposed approach reduces the complexity by as much as 99% (100x of spe…
Learning-Graph-Based Quantum Algorithm for k-distinctness
2012
We present a quantum algorithm solving the $k$-distinctness problem in $O(n^{1-2^{k-2}/(2^k-1)})$ queries with a bounded error. This improves the previous $O(n^{k/(k+1)})$-query algorithm by Ambainis. The construction uses a modified learning graph approach. Compared to the recent paper by Belovs and Lee arXiv:1108.3022, the algorithm doesn't require any prior information on the input, and the complexity analysis is much simpler. Additionally, we introduce an $O(\sqrt{n}\alpha^{1/6})$ algorithm for the graph collision problem where $\alpha$ is the independence number of the graph.
Complexity Selection of the Self-Organizing Map
2002
This paper describes how the complexity of the Self-Organizing Map can be selected using the Minimum Message Length principle. The use of the method in textual data analysis is also demonstrated.
Communication complexity in a 3-computer model
1996
It is proved that the probabilistic communication complexity of the identity function in a 3-computer model isO(√n).
Inductive inference of recursive functions: Complexity bounds
2005
This survey includes principal results on complexity of inductive inference for recursively enumerable classes of total recursive functions. Inductive inference is a process to find an algorithm from sample computations. In the case when the given class of functions is recursively enumerable it is easy to define a natural complexity measure for the inductive inference, namely, the worst-case mindchange number for the first n functions in the given class. Surely, the complexity depends not only on the class, but also on the numbering, i.e. which function is the first, which one is the second, etc. It turns out that, if the result of inference is Goedel number, then complexity of inference ma…
A challenging family of automata for classical minimization algorithms
2010
In this paper a particular family of deterministic automata that was built to reach the worst case complexity of Hopcroft's state minimization algorithm is considered. This family is also challenging for the two other classical minimization algorithms: it achieves the worst case for Moore's algorithm, as a consequence of a result by Berstel et al., and is of at least quadratic complexity for Brzozowski's solution, which is our main contribution. It therefore constitutes an interesting family, which can be useful to measure the efficiency of implementations of well-known or new minimization algorithms.