On-line Learning and the Metrical Task System Problem

The problem of combining expert advice, studied extensively in the Computational Learning Theory literature, and the Metrical Task System (MTS) problem, studied extensively in the area of On-line Algorithms, contain a number of interesting similarities. In this paper we explore the relationship between these problems and show how algorithms designed for each can be used to achieve good bounds and new approaches for solving the other. Specific contributions of this paper include: An analysis of how two recent algorithms for the MTS problem can be applied to the problem of tracking the best expert in the decision-theoretic setting, providing good bounds and an approach of a much different flavor from the well-known multiplicative-update algorithms. An analysis showing how the standard randomized Weighted Majority (or Hedge) algorithm can be used for the problem of combining on-line algorithms on-line, giving much stronger guarantees than the results of Azar, Y., Broder, A., & Manasse, M. (1993). Proc ACM-SIAM Symposium on Discrete Algorithms (pp. 432–440) when the algorithms being combined occupy a state space of bounded diameter. A generalization of the above, showing how (a simplified version of) Herbster and Warmuth's weight-sharing algorithm can be applied to give a finely competitive bound for the uniform-space Metrical Task System problem. We also give a new, simpler algorithm for tracking experts, which unfortunately does not carry over to the MTS problem.Finally, we present an experimental comparison of how these algorithms perform on a process migration problem, a problem that combines aspects of both the experts-tracking and MTS formalisms.     

Deterministic and Randomized Algorithms for Distributed On-Line Task Assignment and Load Balancing without Load Status Information

We find two interesting thresholds for the number of tasks generated under a new model of distributed on-line task assignment and load balancing environment, in which tasks are assigned without any information of current load status and load balancing is achieved together with task assignment. It is shown that balanced load distribution can be obtained deterministically when the number of tasks exceeds the first threshold. Otherwise, a simple randomized strategy can achieve balanced load distribution with high probability if the number of tasks exceeds the second threshold. Received October 30, 2000, and in revised form May 10, 2001. Online publication October 30, 2001.     

Randomized Algorithms for 3-SAT

Schoning proposed a simple yet efficient randomized algorithm for solving the k-SAT problem. In the case of 3-SAT, the algorithm has an expected running time of poly(n)·(4/3)ⁿ = O(1.334ⁿ). In this paper we present randomized algorithms and show that one of them has O(1.3302ⁿ) expected running time, improving Schoning's algorithm. (Note. At this point, the fastest randomized algorithm for 3-SAT is the one given by Iwama and Tamaki that runs in O(1.324ⁿ).)     

Normalization-Based Task Scheduling Algorithms for Heterogeneous Multi-Cloud Environment

Cloud computing is one of the most successful technologies that offer on-demand services through the Internet. However, datacenters of the clouds may not have unlimited capacity which can fulfill the demanded services in peak hours. Therefore, scheduling workloads across multiple clouds in a federated manner has gained a significant attention in the recent years. In this paper, we present four task scheduling algorithms, called CZSN, CDSN, CDN and CNRSN for heterogeneous multi-cloud environment. The first two algorithms are based on traditional normalization techniques, namely z-score and decimal scaling respectively which are hired from data mining. The next two algorithms are based on two newly proposed normalization techniques, called distribution scaling and nearest radix scaling respectively. All the proposed algorithms are shown to work on-line. We perform rigorous experiments on the proposed algorithms using various synthetic as well as benchmark datasets. Their performances are evaluated through simulation run by measuring two performance metrics, namely makespan and average cloud utilization. The experimental results are compared with that of existing algorithms to show the efficacy of the proposed algorithms.     

贪心算法求解k-median问题

文章讨论了用贪心算法解k-m edian问题以及其试验结果。首先提出了一个解k-m edian问题的简单贪心算法,然后对求解质量和求解的近似性能比进行了探讨。主要讨论了公制空间和非公制空间初始解的产生,用贪心算法解k-m edian问题以及全局最优解的计算。试验结果表明:贪心算法解公制空间的k-m edian问题效果要好于解非公制空间的k-m edian问题;用贪心算法解公制空间和非公制空间k-m edian问题都能得到较好的结果。     

Quantum Algorithms for Matching Problems

We present quantum algorithms for the following matching problems in unweighted and weighted graphs with n vertices and m edges:

Models and Scheduling Algorithms for Mixed Data and Task Parallel Programs

An increasing number of scientific programs exhibit two forms of parallelism, often in a nested fashion. At the outer level, the application comprises coarse-grained task parallelism, with dependencies between tasks reflected by an acyclic graph. At the inner level, each node of the graph is a data-parallel operation on arrays. Designers of languages, compilers, and runtime systems are building mechanisms to support such applications by providing processor groups and array remapping capabilities. In this paper we explore how to supplement these mechanisms with policy. What properties of an application, its data size, and the parallel machine determine the maximum potential gains from using both kinds of parallelism? It turns out that large gains can be expected only for specific task graph structures. For such applications, what are practical and effective ways to allocate processors to the nodes of the task graph? In principle one could solve the NP-complete problem of finding the best possible allocation of arbitrary processor subsets to nodes in the task graph. Instead of this, our analysis and simulations show that a simpleswitchedscheduling paradigm, which alternates between pure task and pure data parallelism, provides nearly optimal performance for the task graphs considered here. Furthermore, our scheme is much simpler to implement, has less overhead than the optimal allocation, and would be attractive even if the optimal allocation was free to compute. To evaluate switching in real applications, we implemented a switching task scheduler in the parallel numerical library ScaLAPACK and used it in a nonsymmetric eigenvalue program. Even for fairly large input sizes, the efficiency improves by factors of 1.5 on the Intel Paragon and 2.5 on the IBM SP-2. The remapping and scheduling overhead is negligible, between 0.5 and 5%.     

Randomized Algorithms for Stochastic Approximation under Arbitrary Disturbances

New algorithms for stochastic approximation under input disturbance are designed. For the multidimensional case, they are simple in form, generate consistent estimates for unknown parameters under almost arbitrary disturbances, and are easily incorporated in the design of quantum devices for estimating the gradient vector of a function of several variables.     

Selection Algorithms for Parallel Disk Systems

With the widening gap between processor speeds and disk access speeds, the I/O bottleneck has become critical. Parallel disk systems have been introduced to alleviate this bottleneck. In this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical.     

基于遗传算法的圆柱几何特征信息的测量

研究了各种测量圆柱信息的方法,提出了用遗传算法实现圆柱几何特征信息全局最优解的评定。对需要求的圆柱几何特征信息之间增加约束关系,减少了需要遗传算法评价的参数个数,并提高了遗传算法的收敛速度。建立了用遗传算法实现圆柱度误差最小区域法评定时目标函数数学模型的计算方法。通过实验,在给定不同的遗传算法参数下进行多次评定,该方法都能收敛到全局最优解,并计算稳定,收敛速度快,在计算机上容易实现。     

Server Allocation Algorithms for Tiered Systems

Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a request's total response time is the sum of the response times over all the tiers, many different configurations (number of servers allocated to each tier) can satisfy the expected response-time requirement. Naturally, one would like to find the configuration that minimizes the total system cost while satisfying the total response-time requirement. This is modeled as a non-linear optimization problem using an open-queuing network model of response time, which we call the server allocation problem for tiered systems (SAPTS). In this paper we study the computational complexity of SAPTS and design efficient algorithms to solve it. For a variable number of tiers, we show that the decision version of SAPTS is NP-complete. Then we design a simple two-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS). If the number of tiers is a constant, we show that SAPTS is polynomial-time solvable. Furthermore, we design a fast polynomial-time exact algorithm to solve the important two-tier case. Most of our results extend to the general case in which each tier has an arbitrary response-time function.     

网格任务调度策略研究

网格作为下一代Internet,具有动态性和异构性,如何有效的调度任务是影响网格成功与否的关键技术之一。首先总结了网格计算系统的体系结构和特征,分析了网格任务调度算法的基本原理和性能指标,并对各种调度策略和算法进行了分类和比较,从而为网格任务调度的研究提供了很好的参考价值。     

Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems

The submodular system k-partition problem is a problem of partitioning a given finite set V into k non-empty subsets V ₁,V ₂,…,V _k so that $\sum_{i=1}^{k}f(V_{i})$ is minimized where f is a non-negative submodular function on V. In this paper, we design an approximation algorithm for the problem with fixed k. We also analyze the approximation factor of our algorithm for the hypergraph k-cut problem, which is a problem contained by the submodular system k-partition problem.     

分布式系统中的一类任务分配算法

本文提出了分布式系统中各独立结点根据自身状态和系统反馈进行自适应,以使系统达到最优状态的一种机制。它突破了以往相关工作的一些重要限制,性能得到了很大的改善。