An efficient randomized group testing procedure to determine the number of defectives

In many fault detection problems, we want to detect or identify defective items in a sample set by using the minimum number of tests. Group testing is for the scenario where each test is on a subset of items, and tells whether the subset contains at least one defective item or not. In this paper, we present an efficient randomized group testing procedure that determines the exact number of defectives in a sample set with high success probability.     

四值非线性序集逻辑系统的随机化

利用赋值集的随机化方法,在四值非线性序集逻辑系统L24中提出了公式的随机真度和随机距离,建立了非线性序集逻辑系统上的随机逻辑度量空间.它是计量逻辑学和随机真度的相关理论在非线性序集逻辑系统上的推广.     

On the improvement of allocation rules for multi-armed bandit problem

In this note we present a method to modify allocation rules which is useful for multi-armed bandit problems also for the finite-horizon case. The method is based on monotonicity properties of the value function and the structure of certain optimal policies. It is applied to the well-known allocation rule of Bather (1985). The performance of improvement is investigated by a numerical case study     

测量结果及其不确定度的修约方法

基于国家计量技术规范和实际应用情况,文章提出,为了保证修约值最接近原始数值、修约方法规范统一、易于操作,测量不确定度应统一取成两位有效位数,并据此来修约测量结果.     

带惩罚的容错设施布局问题的近似算法

在带惩罚的容错设施布局问题中, 给定顾客集合、地址集合、以及每个顾客和各个地址之间的连接费用, 这里假设连接费用是可度量的. 每位顾客有各自的服务需求, 每个地址可以开设任意多个设施, 顾客可以被安排连接到某些地址的一些开设的设施上以满足其需求, 也可以被拒绝, 但这时要支付拒绝该顾客所带来的惩罚费用. 目标是确定哪些顾客的服务需求被拒绝并开设一些设施, 将未被拒绝的顾客连接到不同的开设设施上, 使得开设费用、连接费用和惩罚费用总和最小. 给出了带惩罚的容错设施布局问题的线性整数规划及其对偶规划, 进一步, 给出了基于其线性规划和对偶规划舍入的4-近似算法.     

修约间隔规则与回归系数的有效位数

从微小标准偏差准则导出独立测量结果修约间隔的确定规则.考虑回归系数之间强相关性,系数不确定度的有效位数常常需要保留到两位以上.引入有效修约间隔,导出回归系数修约间隔的确定公式,结合实验物理中的多种不同回归类型例子说明了回归系数的有效位数确定方法.     

On randomized algorithms for the majority problem

In the majority problem, we are given n balls coloured black or white and we are allowed to query whether two balls have the same colour or not. The goal is to find a ball of majority colour in the minimum number of queries. The answer is known to be n−B(n) where B(n) is the number of 1’s in the binary representation of n. In this paper we study randomized algorithms for determining majority, which are allowed to err with probability at most ε. We show that any such algorithm must have expected running time at least . Moreover, we provide a randomized algorithm which shows that this result is best possible. These extend a result of De Marco and Pelc [G. De Marco, A. Pelc, Randomized algorithms for determining the majority on graphs, Combin. Probab. Comput. 15 (2006) 823-834].     

Approximation algorithms for the single allocation problem in hub-and-spoke networks and related metric labeling problems

This paper deals with a single allocation problem in hub-and-spoke networks. We present a simple deterministic 3-approximation algorithm and randomized 2-approximation algorithm based on a linear relaxation problem and a randomized rounding procedure. We handle the case where the number of hubs is three, which is known to be NP-hard, and present a (5/4)-approximation algorithm.The single allocation problem includes a special class of the metric labeling problem, defined by introducing an assumption that both objects and labels are embedded in a common metric space. Under this assumption, we can apply our algorithms to the metric labeling problem without losing theoretical approximation ratios. As a byproduct, we also obtain a (4/3)-approximation algorithm for an ordinary metric labeling problem with three labels.