Improved 0/1-interchange scheduling

Consideration is given to the problem of nonpreemptively scheduling a set ofN independent tasks to a system ofM identical processors, with the objective to minimize the overall finish time. It is proved that the 0/1-INTERCHANGE scheduling heuristic can be modified, without increasing its time complexity fromO(N logM), so that its worst-case performance bound is reduced from 2 to 4/3 times optimal.     

A TWO-STAGE SEMI-HYBRID FLOWSHOP PROBLEM IN GRAPHICS PROCESSING

In this paper,a two-stage semi-hybrid flowshop problem which appears in graphics processing is studied. For this problem, there are two machines M1 and M2, and a set of independent jobs J= {J1 ,J2 ,…,Jn }. Each Ji consists of two tasks Ai and Bi ,and task Ai must be completed before task Bi can start. Furthermore ,task Ai can be processed on M1 for ai time units ,or on Mw for ai^J time units ,while task Bi can only be processed on M2 for bi time units. Jobs and machines are available at time zero and no preemption is allowed. The objective is to minimize the maximum job completion time. It is showed that this problem is NP-hard. And a pseudo-polynomial time optimal algorithm is presented. A polynomial time approximation algorithm with worst-case ratio 2 is also presented.     

有两个服务等级的平行机排序问题

对有两个服务等级的平行机排序问题的m台机情形,证明了修正的MF算法的最坏情况界不超过4/3 (1/2)~k,其中k是算法中预先给定的迭代次数.而已有的算法仅为2-1/(m-1),从而大大改进了已有文献中的结果.     

目标为最小化工件运输时间和的单台机器带一个维修时间段的排序问题的一个改进算法

单台机器带一个维修时间段的排序问题,目标是最小化所有工件的运输时间和.在这篇文章里,重新研究了该问题,并给出了一个时间复杂性为O（n³）的近似算法,将性能比从3/2改进到5/4.     

Worst-case analysis of a scheduling algorithm

In this note, a heuristic proposed by Ibarra and Kim (IK) for scheduling independent tasks on unrelated processors is analyzed. The heuristic may create a schedule which finishes a time $\text{m 1 OPT}$, where m is the number of processors, and OPT is the time used in the optimal schedule. This compares unfavorably with the heuristics described by Davis and Jaffe [2], which have worst-case behavior which is $\text{O(OPT 1 m}{}^{0.5}\text{)}$.     

Maximum travelling salesman problem

We present different types of techniques for designing algorithms with worst-case performances for the Maximum Travelling Salesman Problem. Supported by Byelarussian Fundamental Science Found and DAAD     

带机器准备时间的机器覆盖问题的在线、半在线算法

研究以极大化最小机器负载为目标的机器带准备时间的同型机排序问题.证明了LS算法是求解该问题的最好的在线算法,它的最坏情况界为1/m.同时给出了求解两台机的预先知道工件最大加工时间,预先知道工件集的总加工时间以及预先知道工件从大到小到达这三种情形下最好的半在线算法,这三个算法的最坏情况界分别为2/3,2/3以及3/4.     

P‖Cmin随机算法研究

本文研究了P‖Cmin的随机算法及其最坏情况界，我们给出了Pm‖Cmin在线排序问题新的随机上界，并给出了P2‖Cmin的最好随机算法，其最坏情况界为2／3。对P2‖Cmin已知工件加工时间递减半在线模型，我们给出了一最坏情况界为6／7的随机算法并证明了它为最好的。     

HOW GOOD IS A DENSE SHOP SCHEDULE?

In this paper, we study a class of simple and easy-to-construct shop schedules, known as dense schedules. We present tight bounds on the maximum deviation in makespan of dense flow-shop and job-shop schedules from their optimal ones. For dense open-shop schedules, we do the same for the special case of four machines and thus add a stronger supporting case for proving a standing conjecture. Support for the research by the first author is provided by the Management Research Fellowship of the ESRC (Economic & Social Research Council) of U.K., and this research is also partially supported by the National Natural Science Foundation of China.     

Comparative evaluation of heuristic algorithms for the single machine scheduling problem with two operations per job and time-lags

This paper shows that the single machine scheduling problem with multiple operations per job separated by minimum specified time-lags is NP-hard in the strong sense. Seven simple and polynomially bounded heuristic algorithms are developed for its solution when each job requires only two operations. Empirical evaluation shows that the percentage deviation of the heuristic solutions from their lower bounds is quite low and the effectiveness of these heuristic algorithms in finding optimal schedules increases with an increase in the number of jobs.     

带机器准备时间的平行机ordinal排序及近似算法

本文研究带机器准备时间的m台平行机ordinal在线排序问题。讨论了在极小化最大机器完工时间和极小化最大工件完工时间两种目标下的不同下界和相应的在线近似算法。对第一个目标，我们得到了3/2的下界和最坏情况界为2-1/m的近似算法。对第二个目标，我们得到了最坏情况为m的最好近似算法。我们还对一些特殊情况进行了分析。     

带机器准备时间的平行机在线与半在线排序

本文研究带机器准备时间的m台平行机系统在线和半在线排序问题.对在线排序问题,我们证明了LS算法的最坏情况界为2-1/m.对已知工件加工时间递减,已知总加工时间和已知工件最大加工时间三个半在线模型,我们分析了它们的下界和所给算法的最坏情况界.对其中两台机情形均得到了最好近似算怯。     

Worst-case analysis of the differencing method for the partition problem

We prove that the worst-case performance ratio of the Karmarkar-Karp differencing method for the Partition Problem is 7/6     

目标是最小化最大完工时间带柔性维修时间限制的两台机器排序问题的一个近似算法

本文研究了两台机器带柔性维修时间限制的排序问题,其中第一台机器在固定的时间内必须进行维修,而第二台机器一直可用,目标是最小化所有工件的最大完工时间。工件在加工过程中不允许中断。对于该问题,我们给出了一个性能比为的近似算法,并证明了该性能比是紧的。     

一类无干涉作业的码头起重机调度问题的近似算法研究

集装箱港口上的大型货轮通常是由从船头到船尾纵向分布的集装箱船舱构成,而码头起重机主要负责装载或卸载集装箱.如何调度码头起重机在很大程度上影响着集装箱货轮的运输效率.该文主要研究一类无干涉作业的起重机调度问题,目标是极小化装(卸)载总耗时.对三台,四台起重机情形设计了新型调度算法,并给出了最坏情况分析,改进了文献中的已有结果.     

An improved heuristic for one-machine scheduling with delays constraints

An improved heuristic is proposed for one-machine scheduling problem with delay constraints, thus an open problem raised by Wikumet al. is solved. The heuristic solves the corresponding unit-execution-time problem optimally.     

A 3/2 Algorithm for Two-Machine Open Shop with Route-Dependent Processing Times

This paper considers the problem of minimizing the schedule length of a two-machine shop in which not only can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route. This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-case performance ratio of 2. We also present some modifications to this algorithm that improve its performance and guarantee a worst-case performance ratio of 3/2.     

An asymptotic approximation scheme for the concave cost bin packing problem

We consider a generalized one-dimensional bin packing model in which the cost of a bin is a nondecreasing concave function of the utilization of the bin. We show that for any given positive constant ?, there exists a polynomial-time approximation algorithm with an asymptotic worst-case performance ratio of no more than 1 + ?.     

Domination analysis for minimum multiprocessor scheduling

Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P. The domination ratio domr(A,s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We say that P admits an asymptotic domination ratio one (ADRO) algorithm if there is a polynomial time approximation algorithm A for P such that . Alon, Gutin and Krivelevich [Algorithms with large domination ratio, J. Algorithms 50 (2004) 118-131] proved that the partition problem admits an ADRO algorithm. We extend their result to the minimum multiprocessor scheduling problem.