Deterministic and randomized scheduling problems under the lp norm on two identical machines

Parallel machine scheduling problems, which are important discrete optimization problems, may occur in many applications. For example, load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc., are multiprocessor scheduling problem. In the traditional parallel machine scheduling problems, it is assumed that the problems are considered in offline or online environment. But in practice, problems are often not really offline or online but somehow in-between. This means that, with respect to the online problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi-online ones. In this paper, the semi-online problem P2|decr|lp (p＞1) is considered where jobs come in non-increasing order of their processing times and the objective is to minimize the sum of the lp norm of every machine's load. It is shown that LS algorithm is optimal for any lp norm, which extends the results known in the literature. Furthermore, randomized lower bounds for the problems P2|online|lp and P2|decr|lp are presented.     

Using Resampling to Compare Two Proportions

This article shows that when applying resampling methods to the problem of comparing two proportions, students can discover that whether you resample with or without replacement can make a big difference.     

Teaching Statistics through Resampling

This paper describes experiences of teaching statistics without mathematical theory but using computer-intensive re-sampling methods. The method is relevant to statistics teaching at all levels.     

Randomization‐based statistical inference: A resampling and simulation infrastructure

Statistical inference involves drawing scientifically‐based conclusions describing natural processes or observable phenomena from datasets with intrinsic random variation. We designed, implemented, and validated a new portable randomization‐based statistical inference infrastructure ( http://socr.umich.edu/HTML5/Resampling_Webapp ) that blends research‐driven data analytics and interactive learning, and provides a backend computational library for managing large amounts of simulated or user‐provided data. We designed, implemented and validated a new portable randomization‐based statistical inference infrastructure ( http://socr.umich.edu/HTML5/Resampling_Webapp ) that blends research‐driven data analytics and interactive learning, and provides a backend computational library for managing large amounts of simulated or user‐provided data. The core of this framework is a modern randomization webapp, which may be invoked on any device supporting a JavaScript‐enabled web browser. We demonstrate the use of these resources to analyse proportion, mean and other statistics using simulated (virtual experiments) and observed (e.g. Acute Myocardial Infarction, Job Rankings) data. Finally, we draw parallels between parametric inference methods and their distribution‐free alternatives. The Randomization and Resampling webapp can be used for data analytics, as well as for formal, in‐class and informal, out‐of‐the‐classroom learning and teaching of different scientific concepts. Such concepts include sampling, random variation, computational statistical inference and data‐driven analytics. The entire scientific community may utilize, test, expand, modify or embed these resources (data, source‐code, learning activity, webapp) without any restrictions.     

A virtual experience to strengthen students' understanding of inference in experimental design

Although our students correctly define the terms p‐value, Type I and Type II errors, they sometimes misinterpret results from real data. In this work we present an assignment intended to clear up these misconceptions.     

MINITAB MACROS FOR RESAMPLING METHODS

This article describes a set of Minitab macros that perform randomization and bootstrap versions of basic statistical techniques, and suggests ways in which the macros might be used in teaching statistics.     

Resampling with Excel

Standard Microsoft Excel functions and the Excel Data Table facility are used in randomization applications using resampling with and without replacement.     

Deterministic and randomized scheduling problems under the 1p norm on two identical machines

Parallel machine scheduling problems, which are important discrete optimization problems, may occur in many applications. For example, load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc., are multiprocessor scheduling problem. In the traditional parallel machine scheduling problems, it is assumed that the problems are considered in offline or online environment. But in practice, problems are often not really offline or online but somehow in-between. This means that, with respect to the online problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi-online ones. In this paper, the semi-online problemP2|decr|l _p (p>1) is considered where jobs come in non-increasing order of their processing times and the objective is to minimize the sum of thel _p norm of every machine's load. It is shown thatLS algorithm is optimal for anyl _p norm, which extends the results known in the literature. Furthermore, randomized lower bounds for the problemsP2|online|l _p andP2|decr|l _p are presented. Project supported by the National Natural Science Foundation of China (Nos. 10271110, 10301028) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China