Ojas Parekh

Energy Scaling Advantages of Resistive Memory Crossbar Based Computation and Its Application to Sparse Coding

The exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-based architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.

Iterative packing for demand and hypergraph matching

Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems, no single method has emerged that matches the effectiveness and simplicity afforded by the covering case. We offer a simple iterative packing technique that retains features of Jains seminal approach, including the property that the magnitude of the fractional value of the element rounded during each iteration has a direct impact on the approximation guarantee. We apply iterative packing to generalized matching problems including demand matching and k-column-sparse column-restricted packing (k-CS-PIP) and obtain approximation algorithms that essentially settle the integrality gap for these problems. We present a simple deterministic 2k-approximation for k-CSPIP, where an 8k-approximation was the best deterministic algorithm previously known. The integrality gap in this case is at least 2(k-1+1/k). We also give a deterministic 3-approximation for a generalization of demand matching, settling its natural integrality gap.

On Partial Vertex Cover and Budgeted Maximum Coverage Problems in Bipartite Graphs

Graphs are often used to model risk management in various systems. Particularly, Caskurlu et al. in [6] have considered a system which essentially represents a tripartite graph. The goal in this model is to reduce the risk in the system below a predefined risk threshold level. It can be shown that the main goal in this risk management system can be formulated as a Partial Vertex Cover problem on bipartite graphs. It is well-known that the vertex cover problem is in P on bipartite graphs; however, the computational complexity of the partial vertex cover problem on bipartite graphs is open. In this paper, we show that the partial vertex cover problem is NP-hard on bipartite graphs. Then, we show that the budgeted maximum coverage problem (a problem related to partial vertex cover problem) admits an (frac{8}{9})-approximation algorithm in the class of bipartite graphs, which matches the integrality gap of a natural LP relaxation.

Generalized Hypergraph Matching via Iterated Packing and Local Ratio

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A computational framework for ontologically storing and analyzing very large overhead image sets

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LDRD final report on massively-parallel linear programming : the parPCx system.

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An approximation algorithm for the edge-dilation k-center problem

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Spiking network algorithms for scientific computing

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Constant-Depth and Subcubic-Size Threshold Circuits for Matrix Multiplication

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A combinatorial model for dentate gyrus sparse coding

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