Approximation algorithms for stochastic scheduling problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. [109]-113).In this dissertation we study a broad class of stochastic scheduling problems characterized by the presence of hard deadline constraints. The input to such a problem is a set of jobs, each with an associated value, processing time, and deadline. We would like to schedule these jobs on a set of machines over time. In our stochastic setting, the processing time of each job is random, known in advance only as a probability distribution (and we make no assumptions about the structure of this distribution). Only after a job completes do we know its actual "instantiated" processing time with certainty. Each machine can process only a singe job at a time, and each job must be assigned to only one machine for processing. After a job starts processing we require that it must be allowed to complete - it cannot be canceled or "preempted" (put on hold and resumed later). Our goal is to devise a scheduling policy that maximizes the expected value of jobs that are scheduled by their deadlines. A scheduling policy observes the state of our machines over time, and any time a machine becomes available for use, it selects a new job to execute on that machine. Scheduling policies can be classified as adaptive or non-adaptive based on whether or not they utilize information learned from the instantiation of processing times of previously-completed jobs in their future scheduling decisions. A novel aspect of our work lies in studying the benefit one can obtain through adaptivity, as we show that for all of our stochastic scheduling problems, adaptivity can only allow us to improve the expected value obtained by an optimal policy by at most a small constant factor. All of the problems we consider are at least NP-hard since they contain the deterministic 0/1 knapsack problem as a special case. We therefore seek to develop approximation algorithms: algorithms that run in polynomial time and compute a policy whose expected value is provably close to that of an optimal adaptive(cont.) policy. For all the problems we consider, we can approximate the expected value obtained by an optimal adaptive policy to within a small constant factor (which depends on the problem under consideration, but is always less than 10). A small handful of our results are pseudo-approximation algorithms, delivering an approximately optimal policy that is feasible with respect to a slightly expanded set of deadlines. Our algorithms utilize a wide variety of techniques, ranging from fairly well-established methods like randomized rounding to more novel techniques such as those we use to bound the expected value obtained by an optimal adaptive policy. In the scheduling literature to date and also in practice, the "deadline" of a job refers to the time by which a job must be completed. We introduce a new model, called the start deadline model, in which the deadline of a job instead governs the time by which we must start the job. While there is no difference between this model and the standard "completion deadline" model in a deterministic setting, we show that for our stochastic problems, one can generally obtain much stronger approximation results with much simpler analyses in the start deadline model. The simplest problem variant we consider is the so-called stochastic knapsack problem, where all jobs share a common deadline and we schedule them on a single machine. The most general variant we consider involves scheduling jobs with individual deadlines on a set of "unrelated" parallel machines, where the value of a job and its processing time distribution can vary depending on the machine to which it is assigned.(cont.) We also discuss algorithms based on dynamic programming for stochastic scheduling problems and their relatives in a discrete-time setting (where processing times are small integers), and we show how to use a new technique from signal processing called zero-delay convolution to improve the running time of dynamic programming algorithms for some of these problems.by Brian Christopher Dean.Ph.D

Annual Report of the University, 2007-2008, Volumes 1-6

Project Summary and Goals Historically, affirmative action policies have evolved from initial programs aimed at providing equal educational opportunities to all students, to the legitimacy of programs that are aimed at achieving diversity in higher education. In June 2003, a U.S. Supreme Court ruling on affirmative action pushed higher education across the threshold toward creating a new paradigm for diversity in the 21 51 century. The court clearly stale that affirmative action is still viable but that our institutions must reconsider our traditional concepts for building diversity in the next few decades. This shift in historical context of diversity in our society has led to an important objective: If a diverse student body is an essential factor in a quality higher education, then it is imperative that elementary, secondary and undergraduate schools fulfill their missions to successfully educate a diverse population. In NM, the success of graduate programs depends on the state\u27s P-12 schools, the community and institutions of higher education, and their shared task of educating all students. Further, when the lens in broadened to view the entire P - 20 educational pipeline, it becomes apparent that the loss of students from elementary school to high school is enormous, constricting the number of students who go on to college. Not only are these of concern to what is happening in terms of their academic education but as well in terms of the communities that are affected to make critical decision and become and stay involved in the political and policy world that affects them. Guiding Principles Engaging Latino Communities for Education New Mexico (ENLACE NM) is a statewide collaboration of gente who represent the voices of underrepresented children and families- people who have historically not had a say in policy initiatives that directly impact them and their communities. Therefore, they, and others from our community, are at the forefront of this initiative. We have developed this collaboration based on a process that empowers these communities to find their voice in the pursuit of social justice and educational access, equity and success

A study of the provision of distance education for the upgrading and improvement of the qualifications of teachers in the province of Kwazulu-Natal

This research is predicated in the firm conviction that the quality of education is dependent upon the quality of teachers. Teachers as the bedrock of education must participate actively and conscientiously in their intellectual growth through various forms of INSET discussed in the research. From an international comparative perspective DE as a strategy of INSET is deemed as the most functional, if not prudent and efficacious educational experience for the upgrading and improvement of the qualifications of teachers. In this research the origin of DE in terms of its antecedents and evolution, the raison d'etre and the advantages and limitations of DE are adumbrated in order to focus on the complexity and diversity of DE. As part of the conceptual and theoretical framework various terms used synonymously with DE are considered. A syntagma of principles providing a utilitarian and pragmatic connotation for DE is then postulated. Selected theories relevant to DE provide the synthesis for theoretical perspectives. The typology of DE institutions comprising autonomous, dedicated providers of DE and those that are mixed or hybrid or dual mode systems is analyzed. In koeping with the theme of educational borrowing fundamental to comparative education studies provision of DE by the UKOU and AU for developed countries, IGNOU and the ZINTEC model for developing countries is discussed. National examples are UNISA, Vista University and SACTE. The provincial institutions discussed are the former SCE, NCE, UCFE and the newly formed SACOL. General and specific recommendations for the provision of DE programmes for the upgrading and improvement of the qualifications of teachers in the Province of KwaZulu-Natal are adumbrated. By way of conclusion, it is iterated that the provision of DE for the upgrading and improvement of the qualifications of teachers is irrefragably xxvii the quintessential factor in the new generation of teacher education and a pivotal element for INSET.Educational StudiesD. Ed. (Comparative Education

Bowdoin Orient v.137, no.1-25 (2007-2008)

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