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
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Allocation Algorithms for Networks with Scarce Resources(2015) Sarpatwar, Kanthi Kiran; Khuller, Samir; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Many fundamental algorithmic techniques have roots in applications to computer networks. We consider several problems that crop up in wireless ad hoc networks, sensor networks, P2P networks, and cluster networks. The common challenge here is to deal with certain bottleneck resources that are crucial for performance of the underlying system. Broadly, we deal with the following issues. Data: The primary goal in resource replication problems is to replicate data objects on server nodes with limited storage capacities, so that the latency of client nodes needing these objects is minimized. Previous work in this area is heuristic and without guarantees. We develop tight (or nearly) approximation algorithms for several problems including basic resource replication - where clients need all objects and server can store at most one object, subset resource replication - where clients require different subsets of objects and servers have limited non-uniform capacity, and related variants. Computational resources: To facilitate packing of jobs needing disparate amounts of computational resources in cluster networks, an important auxiliary problem to solve is that of container selection. The idea is to select a limited number of ``containers'' that represent a given pool of jobs while minimizing ``wastage'' of resources. Subsequently, containers representing jobs can be packed instead of jobs themselves. We study this problem in two settings: continuous - where there are no additional restrictions on chosen containers, and discrete - where we must choose containers from a given set. We show that the continuous variant is NP-hard and admits a polynomial time approximation scheme. Contrastingly, the discrete variant is shown to be NP-hard to approximate. Therefore, we seek bi-approximation algorithms for this case. Energy resources: Wireless ad hoc networks contain nodes with limited battery life and it is crucial to design energy efficient algorithms. We obtain tight approximation (up to constant factors) guarantees for partial and budgeted versions of the connected dominating set problem, which is regarded as a good model for a virtual backbone of a wireless ad hoc network. Further, we will discuss approximation algorithms for some problems involving target monitoring in sensor networks and message propagation in radio networks. We will end with a discussion on future work.Item Approximation Algorithms for Resource Allocation(2011) Saha, Barna; Khuller, Samir; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis is devoted to designing new techniques and algorithms for combinatorial optimization problems arising in various applications of resource allocation. Resource allocation refers to a class of problems where scarce resources must be distributed among competing agents maintaining certain optimization criteria. Examples include scheduling jobs on one/multiple machines maintaining system performance; assigning advertisements to bidders, or items to people maximizing profit/social fairness; allocating servers or channels satisfying networking requirements etc. Altogether they comprise a wide variety of combinatorial optimization problems. However, a majority of these problems are NP-hard in nature and therefore, the goal herein is to develop approximation algorithms that approximate the optimal solution as best as possible in polynomial time. The thesis addresses two main directions. First, we develop several new techniques, predominantly, a new linear programming rounding methodology and a constructive aspect of a well-known probabilistic method, the Lov\'{a}sz Local Lemma (LLL). Second, we employ these techniques to applications of resource allocation obtaining substantial improvements over known results. Our research also spurs new direction of study; we introduce new models for achieving energy efficiency in scheduling and a novel framework for assigning advertisements in cellular networks. Both of these lead to a variety of interesting questions. Our linear programming rounding methodology is a significant generalization of two major rounding approaches in the theory of approximation algorithms, namely the dependent rounding and the iterative relaxation procedure. Our constructive version of LLL leads to first algorithmic results for many combinatorial problems. In addition, it settles a major open question of obtaining a constant factor approximation algorithm for the Santa Claus problem. The Santa Claus problem is a $NP$-hard resource allocation problem that received much attention in the last several years. Through out this thesis, we study a number of applications related to scheduling jobs on unrelated parallel machines, such as provisionally shutting down machines to save energy, selectively dropping outliers to improve system performance, handling machines with hard capacity bounds on the number of jobs they can process etc. Hard capacity constraints arise naturally in many other applications and often render a hitherto simple combinatorial optimization problem difficult. In this thesis, we encounter many such instances of hard capacity constraints, namely in budgeted allocation of advertisements for cellular networks, overlay network design, and in classical problems like vertex cover, set cover and k-median.