Improving multikey Quicksort for sorting strings with many equal elements

Bentley and Sedgewick proposed multikey Quicksort with ‘split-end’ partitioning for sorting strings. But it can be slow in case of many equal elements because it adopted ‘split-end’ partitioning that moves equal elements to the ends and swaps back to the middle. We present ‘collect-center’ partitioning to improve multikey Quicksort in that case. It moves equal elements to the middle directly like the ‘Dutch National Flag Problem’ partitioning approach and it uses two inner loops like Bentley and McIlroy's. In case of many equal elements such as DNA sequences, HTML files, and English texts, multikey Quicksort with ‘collect-center’ partitioning is faster than multikey Quicksort with ‘split-end’ partitioning.     

A retunable PID multi-rate controller for a networked control system

This paper introduces a control strategy based on retuning a multi-rate PID controller in accordance with the variable delays detected in a networked control system, in order to avoid a decreased control performance. The basic idea is minimising the first-order Taylor terms of a performance measure via gain scheduling, i.e., making the controller gains delay dependent. As network delay is time-variant, the stability of this control approach will be proved by means of linear matrix inequalities.     

Distributed evolutionary multi-objective mesh-partitioning algorithm for parallel finite element computations

Majority of the mesh-partitioning algorithms attempt to optimise the interprocessor communications, while balancing the computational load among the processors. However, it is desirable to simultaneously optimise the submesh aspect ratios in order to significantly improve the convergence characteristics of the domain decomposition based Preconditioned-conjugate-gradient algorithms, being used extensively in the state-of-the-art parallel finite element codes. Keeping this in view, a new distributed multi-objective mesh-partitioning algorithm using evolutionary computing techniques is proposed in this paper. Effectiveness of the proposed distributed mesh-partitioning algorithm is demonstrated by solving several unstructured meshes of practical-engineering problems and also benchmark problems.     

Convergence of non-autonomous discrete-time Hopfield model with delays

This paper is concerned with boundedness, convergence of solution of a class of non-autonomous discrete-time delayed Hopfield neural network model. Using the inequality technique, we obtain some sufficient conditions ensuring the boundedness of solutions of the discrete-time delayed Hopfield models in time-varying situation. Then, by exploring intrinsic features between non-autonomous system and its asymptotic equations, several novel sufficient conditions are established to ensure that all solutions of the networks converge to the solution of its asymptotic equations. Especially, for case of asymptotic autonomous system or asymptotic periodic system, we obtain some sufficient conditions ensuring all solutions of original system convergent to equilibrium or periodic solution of asymptotic system, respectively. An example is provided for demonstrating the effectiveness of the global stability conditions presented. Our results are not only presented in terms of system parameters and can be easily verified but also are less restrictive than previously known criteria.     

一种时延受限的最优时延抖动路由算法

研究多播端到端时延受限条件下的最优时延抖动问题,提出一种有效的多播路由算法。通过修改源节点到目的节点的路径,使时延较小的目的节点获得尽可能大的时延值,时延较大的目的节点获得尽可能小的时延值。仿真结果表明,该算法能获得较小的时延抖动。     

基于Ad Hoc的改进型多信道接入协议研究

为了解决目前多信道接入协议面临的多信道隐藏终端和多信道Deafness问题,加入了探测报文和等待报文,采用节点状态表和信道空闲状态表的方法,并采用NS2仿真软件对该协议进行性能仿真。仿真结果表明,该协议解决了多信道隐藏终端和多信道Deafness问题,与DPC协议相比提高了网络吞吐量和信道利用率,降低了网络传输的延迟,增强了网络的性能。     

一种松弛的优化均衡流式图划分算法研究

在大规模图数据的分布式处理中,往往需要将图数据进行划分并放置在不同的节点上。如果数据划分得不均衡,那么部分节点可能会成为分布式系统的瓶颈。为了提高图数据划分的均衡性,并且有效地应对图数据的快速更新,提出了一种松弛的优化均衡流式图划分算法。首先,定义了一种同时包含划分内部代价和划分之间的割的代价的目标函数作为图划分的整体框架。然后,在图划分框架的基础上通过最大化和最小化两种优化函数分析了均衡图划分问题,并给出了二者之间的关系。最后,针对流式图数据,提出一种贪婪的图最优k划分算法。该划分算法以最大化优化函数为基础,通过最大化顶点放置产生的目标函数增加值进行节点划分块的选取。实验表明,提出的图划分算法与相关算法相比,不仅均衡性好,而且通信开销小,在基于该算法进行图划分时上层应用的计算性能得到了明显的提高。     

Approximation algorithms for the Weighted t-Uniform Sparsest Cut and some other graph partitioning problems

We study the Weighted t-Uniform Sparsest Cut (Weighted t-USC) and other related problems. In an instance of the Weighted t-USC problem, a parameter t and an undirected graph $G=(V,E)$ with edge-weights $w:E\to {\mathbb{R}}_{\ge 0}$ and vertex-weights $\eta :V\to {\mathbb{R}}_{+}$ are given. The goal is to find a vertex set $S\subseteq V$ with $|S|\le t$ while minimizing $w(S,V\backslash S)/\eta (S)$, where $w(S,V\backslash S)$ is the total weight of the edges with exactly one endpoint in S and $\eta (S)={\sum }_{v\in S}\eta (v)$. For this problem, we present a $(O(\log t),1+ϵ)$ factor bicriteria approximation algorithm. Our algorithm outperforms the current best algorithm when $t=n^{o(1)}$. We also present better approximation algorithms for Weighted ρ-Unbalanced Cut and Min–Max k-Partitioning problems.     

基于最小割图分割的社区发现算法

该文证明了模块度最大化问题可以被转换成为原网络上的最小割图分割问题,并且基于该证明提出了一种高效的社区发现算法。同时,该文创新性地将模块度理论与当今比较流行的统计推理模型相结合: 首先,这些统计推理模型被转化为模块度最大化问题中的零模型;其次,统计推理模型中的目标函数被修改并应用于本文的最优化算法中。实验结果显示,无论是在真实世界网络还是在人工生成网络中,该文提出的算法均具有高效和稳定的发现社区的能力。