Vishwanath, SriramCaramanis, Constantine2015-11-042018-01-222015-11-042018-01-222015-08August 201http://hdl.handle.net/2152/32226textOur unprecedented capacity for data generation and acquisition often reaches the limits of our data storage capabilities. Situations when data are generated faster or at a greater volume than can be stored demand a streaming approach. Memory is an even more valuable resource. Algorithms that use more memory than necessary can pose bottlenecks when processing high-dimensional data and the need for memory-efficient algorithms is especially stressed in the streaming setting. Finally, network along with storage, emerge as the critical bottlenecks in the context of distributed computation. These computational constraints spell out a demand for efficient tools that guarantee a solution in the face of limited resources, even when the data is very noisy or highly incomplete. For the first part of this dissertation, we present our work on streaming, memory-limited Principal Component Analysis (PCA). Therein, we give the first convergence guarantees for an algorithm that solves PCA in the single-pass streaming setting. Then, we discuss the distinct challenges that arise when the received samples are overwhelmingly incomplete and present an algorithm and analysis that deals with this issue. Finally, we give a set of extensive experiment results that showcase the practical merits of our algorithm over the state of the art. The need for heavy network communication arises as the bottleneck when dealing with cluster computation. In that paradigm, a set of worker nodes are connected over the network to produce a cluster with improved computational and storage capacities. This comes with an increased need for communication across the network. In the last part of this work, we consider the problem of PageRank on graph engines. Therein, we make changes to GraphLab, a state-of-the-art platform for distributed graph computation, in a way that leads to a 7x-10x speedup for certain PageRank approximation tasks. Accompanying analysis supports the behaviour we see in our experiments.application/pdfenResource contraintsLimited memoryStorageNetworkPrinciple component analysisPageRankGraph enginesThesis2015-11-04