794 research outputs found

    05031 Abstracts Collection -- Algorithms for Optimization with Incomplete Information

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    From 16.01.05 to 21.01.05, the Dagstuhl Seminar 05031 ``Algorithms for Optimization with Incomplete Information\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

    Simple and effective dynamic provisioning for power-proportional data centers.

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    数据中心在运转过程中需要消耗大量的电能。但是这其中的很大一部分电能都在工作负荷少时被空闲的服务器消耗了。动态供应技术通过在工作负荷少时,关掉不必要的服务器来节省这一部分的电能。在这篇文章中,我们研究未来工作负荷信息到底能给动态供应带来多大好处。特别地,对于有或没有未来工作负荷信息的两种情况,我们提出了在线的动态供应算法。我们首先发现了离线动态供应的最优解有一个很优美的结构,通过这个优美的结构我们可以以分而治之的方法完全确定离线动态供应的最优解。在这个基础之上我们设计了两个在线算法,它们的竞争比分别为2-α和e/(e - 1 + α),其中α表示标准化的预测未来窗口的长度。在这个预测未来窗口中,未来的工作负荷信息可以精确的获得。一个重要的发现是超出一个完整的预测未来窗口的未来工作负荷信息不会对动态供应的性能有任何提高。我们提出的在线算法是分散的,因此易于实现。最后,我们用真是数据中心的数据测试了我们的在线算法。在设计在线算法的时候,我们利用了未来工作负荷信息。这是因为在很多的现代系统中,短期的未来工作信息可以被精确的估计。我们也测试了我们的算法在有预测噪声时候的性能,结果表明我们的算法在有噪声时,也能很好的工作。我们相信利用未来信息是设计在线算法的一个新的角度。在传统的在线算法设计过程中,我们通常不考虑未来输入信息。在这种情况下,许多在线问题有简单的最优的算法,但是这个最优算法的竞争比却很大。其实未来输入信息在很多在线问题中都能在一定程度上被精确预测,所以我们相信我们可以利用这些未来输入信息去设计竞争比较小的在线算法,这样设计的在线算法具有更多的应用优点,并在理论上也给予我们启发。Energy consumption represents a significant cost in data center operation. A large fraction of the energy however, is used to power idle servers when the workload is low. Dynamic provisioning techniques aim at saving this portion of the energy by turning of unnecessary servers. In this thesis we explore how much gain knowing future workload information can bring to dynamic pro-visioning. In particular we develop online dynamic provisioning solutions with and without future workload information available. We first reveal an elegant structure of the offline dynamic pro-visioning problem which allows us to characterize the optimal solution in a "divide-and-conquer" manner. We then exploit this insight to design two online algorithms with competitive ratios 2 - α and e/ (e - 1+ α), respectively where 0 ≤ α ≤ 1 is the normalized size of a look-ahead window in which future workload information is available. A fundamental observation is that future workload information beyond the full-size look-ahead window (corresponding to α =1) will not improve dynamic provisioning performance. Our algorithms are decentralized and easy to im-plement. We demonstrate their effectiveness in simulations using real-world traces.When designing online algorithms, we utilize future input information because for many modern systems their short-term future inputs can be predicted by machine learning time-series analysis etc. We also test our algorithms in the presence of prediction errors in future workload information and the results show that our algorithms are robust to prediction errors. We believe that utilizing future information is a new and important degree of freedom in designing online algorithms. In traditional online algo¬rithm design future input information is not taken into account. Many online problems have online algorithms with optimal but large competitive ratios. Since future input information to some extent can be estimated accurately in many problems we believe that we should exploit such information in online algorithm design to achieve better competitive ratio and provide more competitive edge in both practice and theory.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Lu, Tan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2012.Includes bibliographical references (leaves 76-81).Abstracts also in Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Contributions --- p.4Chapter 1.3 --- Thesis Organization --- p.5Chapter 2 --- Related Work --- p.6Chapter 3 --- Problem Formulation --- p.10Chapter 3.1 --- Settings and Models --- p.10Chapter 3.2 --- Problem Formulation --- p.13Chapter 4 --- Optimal Solution and Offline Algorithm --- p.15Chapter 4.1 --- Structure of Optimal Solution --- p.15Chapter 4.2 --- Intuitions and Observations --- p.17Chapter 4.3 --- Offline Algorithm Achieving the Optimal Solution --- p.18Chapter 5 --- Online Dynamic Provisioning --- p.21Chapter 5.1 --- Dynamic Provisioning without FutureWorkload Information --- p.22Chapter 5.2 --- Dynamic Provisioning with Future Workload Information --- p.23Chapter 5.3 --- Adapting the Algorithms to Work with Discrete-Time Fluid Workload Model --- p.31Chapter 5.4 --- Extending to Case Where Servers Have Setup Time --- p.32Chapter 6 --- Experiments --- p.35Chapter 6.1 --- Settings --- p.35Chapter 6.2 --- Performance of the Proposed Online Algorithms --- p.38Chapter 6.3 --- Impact of Prediction Error --- p.39Chapter 6.4 --- Impact of Peak-to-Mean Ratio (PMR) --- p.40Chapter 6.5 --- Discussion --- p.40Chapter 6.6 --- Additional Experiments --- p.41Chapter 7 --- A New Degree of Freedom for Designing Online Algorithm --- p.44Chapter 7.1 --- The Lost Cow Problem --- p.45Chapter 7.2 --- Secretary Problem without Future Information --- p.47Chapter 7.3 --- Secretary Problem with Future Information --- p.48Chapter 7.4 --- Summary --- p.50Chapter 8 --- Conclusion --- p.51Chapter A --- Proof --- p.54Chapter A.1 --- Proof of Theorem 4.1.1 --- p.54Chapter A.2 --- Proof of Theorem 4.3.1 --- p.57Chapter A.3 --- Least idle vs last empty --- p.60Chapter A.4 --- Proof of Theorem 5.2.2 --- p.61Chapter A.5 --- Proof of Corollary 5.4.1 --- p.70Chapter A.6 --- Proof of Lemma 7.1.1 --- p.72Chapter A.7 --- Proof of Theorem 7.3.1 --- p.74Bibliography --- p.7

    A Match in Time Saves Nine: Deterministic Online Matching With Delays

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    We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays. We present the first deterministic online algorithm for this problem. Its competitive ratio is O(mlog25.5)O(m^{\log_2 5.5}) =O(m2.46) = O(m^{2.46}), where 2m2 m is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance

    Essays on valuing non-market goods in imperfectly competitive markets

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    Debates on climate change have conceded to most parties acknowledging the existence of negative impacts of changing weather patterns. However, these impacts have not fully been assessed. One way which changing climates can negatively impact an economy is by changing the market structures of its most influential industries; making these markets more imperfectly competitive and taking value away from consumers. This dissertation draws on this fact and suggests accurate ways to both identify and quantify the costs of climate change. In the first chapter of this dissertation, the ski industry is used as a case study. A unique data set along with the econometric technique of discrete time survival analysis is used to estimate the impact of weather on the survival of ski areas over time. Results suggest that changing weather patterns have been an influential factor in the closure of many ski areas throughout the region. For this reason, the ski industry has become much less competitive allowing ski area managers to increase the price of their lift tickets over their marginal costs. The second chapter builds off the first to show that since many of the industries which are vulnerable to climate change are imperfectly competitive in nature, there is a need to more precise theoretical techniques of valuing non-market, climate related goods in these industries in which firms can artificially increase the price. Huang (2013) builds off of Feenstra (1995) and adapts the traditional hedonic valuation method to account for imperfect competition in the market. The theoretical technique is discussed and employed against current approaches to show its feasibility in measuring the true value of goods which are marked up when firms enjoy market power. Together the two chapters of this dissertation develop a strategy for increased precision in the measurement of the costs of climate change. By first identifying vulnerable industries with the econometric techniques used in chapter one and then estimating the value of the climate related goods in these industries with the model presented in chapter two, researchers could determine important factors which have the ability to influence policy debates on climate change

    Semi-online algorithms for power-aware load balancing

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    Proportionally Fair Online Allocation of Public Goods with Predictions

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    We design online algorithms for the fair allocation of public goods to a set of NN agents over a sequence of TT rounds and focus on improving their performance using predictions. In the basic model, a public good arrives in each round, the algorithm learns every agent's value for the good, and must irrevocably decide the amount of investment in the good without exceeding a total budget of BB across all rounds. The algorithm can utilize (potentially inaccurate) predictions of each agent's total value for all the goods to arrive. We measure the performance of the algorithm using a proportional fairness objective, which informally demands that every group of agents be rewarded in proportion to its size and the cohesiveness of its preferences. In the special case of binary agent preferences and a unit budget, we show that O(logN)O(\log N) proportional fairness can be achieved without using any predictions, and that this is optimal even if perfectly accurate predictions were available. However, for general preferences and budget no algorithm can achieve better than Θ(T/B)\Theta(T/B) proportional fairness without predictions. We show that algorithms with (reasonably accurate) predictions can do much better, achieving Θ(log(T/B))\Theta(\log (T/B)) proportional fairness. We also extend this result to a general model in which a batch of LL public goods arrive in each round and achieve O(log(min(N,L)T/B))O(\log (\min(N,L) \cdot T/B)) proportional fairness. Our exact bounds are parametrized as a function of the error in the predictions and the performance degrades gracefully with increasing errors

    Energy sustainable paradigms and methods for future mobile networks: A survey

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    In this survey, we discuss the role of energy in the design of future mobile networks and, in particular, we advocate and elaborate on the use of energy harvesting (EH) hardware as a means to decrease the environmental footprint of 5G technology. To take full advantage of the harvested (renewable) energy, while still meeting the quality of service required by dense 5G deployments, suitable management techniques are here reviewed, highlighting the open issues that are still to be solved to provide eco-friendly and cost-effective mobile architectures. Several solutions have recently been proposed to tackle capacity, coverage and efficiency problems, including: C-RAN, Software Defined Networking (SDN) and fog computing, among others. However, these are not explicitly tailored to increase the energy efficiency of networks featuring renewable energy sources, and have the following limitations: (i) their energy savings are in many cases still insufficient and (ii) they do not consider network elements possessing energy harvesting capabilities. In this paper, we systematically review existing energy sustainable paradigms and methods to address points (i) and (ii), discussing how these can be exploited to obtain highly efficient, energy self-sufficient and high capacity networks. Several open issues have emerged from our review, ranging from the need for accurate energy, transmission and consumption models, to the lack of accurate data traffic profiles, to the use of power transfer, energy cooperation and energy trading techniques. These challenges are here discussed along with some research directions to follow for achieving sustainable 5G systems.Comment: Accepted by Elsevier Computer Communications, 21 pages, 9 figure

    A survey of statistical network models

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    Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
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