Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Primal-Dual Techniques for Online Algorithms and Mechanisms(2015) Liaghat, Vahid; Hajiaghayi, MohammadTaghi; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An offline algorithm is one that knows the entire input in advance. An online algorithm, however, processes its input in a serial fashion. In contrast to offline algorithms, an online algorithm works in a local fashion and has to make irrevocable decisions without having the entire input. Online algorithms are often not optimal since their irrevocable decisions may turn out to be inefficient after receiving the rest of the input. For a given online problem, the goal is to design algorithms which are competitive against the offline optimal solutions. In a classical offline scenario, it is often common to see a dual analysis of problems that can be formulated as a linear or convex program. Primal-dual and dual-fitting techniques have been successfully applied to many such problems. Unfortunately, the usual tricks come short in an online setting since an online algorithm should make decisions without knowing even the whole program. In this thesis, we study the competitive analysis of fundamental problems in the literature such as different variants of online matching and online Steiner connectivity, via online dual techniques. Although there are many generic tools for solving an optimization problem in the offline paradigm, in comparison, much less is known for tackling online problems. The main focus of this work is to design generic techniques for solving integral linear optimization problems where the solution space is restricted via a set of linear constraints. A general family of these problems are online packing/covering problems. Our work shows that for several seemingly unrelated problems, primal-dual techniques can be successfully applied as a unifying approach for analyzing these problems. We believe this leads to generic algorithmic frameworks for solving online problems. In the first part of the thesis, we show the effectiveness of our techniques in the stochastic settings and their applications in Bayesian mechanism design. In particular, we introduce new techniques for solving a fundamental linear optimization problem, namely, the stochastic generalized assignment problem (GAP). This packing problem generalizes various problems such as online matching, ad allocation, bin packing, etc. We furthermore show applications of such results in the mechanism design by introducing Prophet Secretary, a novel Bayesian model for online auctions. In the second part of the thesis, we focus on the covering problems. We develop the framework of "Disk Painting" for a general class of network design problems that can be characterized by proper functions. This class generalizes the node-weighted and edge-weighted variants of several well-known Steiner connectivity problems. We furthermore design a generic technique for solving the prize-collecting variants of these problems when there exists a dual analysis for the non-prize-collecting counterparts. Hence, we solve the online prize-collecting variants of several network design problems for the first time. Finally we focus on designing techniques for online problems with mixed packing/covering constraints. We initiate the study of degree-bounded graph optimization problems in the online setting by designing an online algorithm with a tight competitive ratio for the degree-bounded Steiner forest problem. We hope these techniques establishes a starting point for the analysis of the important class of online degree-bounded optimization on graphs.Item ROBUST REVENUE MANAGEMENT WITH LIMITED INFORMATION : THEORY AND EXPERIMENTS(2009) Lan, Yingjie; Ball, Michael O; Karaesmen, Itir A; Business and Management: Decision & Information Technologies; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Revenue management (RM) problems with full probabilistic information are well studied. However, as RM practice spreads to new businesses and industries, there are more and more applications where no or only limited information is available. In that respect, it is highly desirable to develop models and methods that rely on less information, and make fewer assumptions about the underlying uncertainty. On the other hand, a decision maker may not only lack data and accurate forecasting in a new application, but he may have objectives (e.g. guarantees on worst-case profits) other than maximizing the average performance of a system. This dissertation focuses on the multi-fare single resource (leg) RM problem with limited information. We only use lower and upper bounds (i.e. a parameter range), instead of any particular probability distribution or random process to characterize an uncertain parameter. We build models that guarantee a certain performance level under all possible realizations within the given bounds. Our methods are based on the regret criterion, where a decision maker compares his performance to a perfect hindsight (offline) performance. We use competitive analysis of online algorithms to derive optimal static booking control policies that either (i) maximize the competitive ratio (equivalent to minimizing the maximum regret) or (ii) minimize the maximum absolute regret. Under either criterion, we obtain closed-form solutions and investigate the properties of optimal policies. We first investigate the basic multi-fare model for booking control, assuming advance reservations are not cancelled and do not become no-shows. The uncertainty in this problem is in the demand for each fare class. We use information on lower and upper bounds of demand for each fare class. We determine optimal static booking policies whose booking limits remain constant throughout the whole booking horizon. We also show how dynamic policies, by adjusting the booking limits at any time based on the bookings already on hand, can be obtained. Then, we integrate overbooking decisions to the basic model. We consider two different models for overbooking. The first one uses limited information on no-shows; again the information being the lower and upper bound on the no-show rate. This is appropriate for situations where there is not enough historical data, e.g. in a new business. The second model differs from the first by assuming the no-show process can be fully characterized with a probabilistic model. If a decision-maker has uncensored historical data, which is often the case in reality, he/she can accurately estimate the probability distribution of no-shows. The overbooking and booking control decisions are made simultaneously in both extended models. We derive static overbooking and booking limits policies in either case. Extensive computational experiments show that the proposed methods that use limited information are very effective and provide consistent and robust results. We also show that the policies produced by our models can be used in combination with traditional ones to enhance the system performance.