Doctor of Philosophy

dissertationSparse matrix codes are found in numerous applications ranging from iterative numerical solvers to graph analytics. Achieving high performance on these codes has however been a significant challenge, mainly due to array access indirection, for example, of the form A[B[i]]. Indirect accesses make precise dependence analysis impossible at compile-time, and hence prevent many parallelizing and locality optimizing transformations from being applied. The expert user relies on manually written libraries to tailor the sparse code and data representations best suited to the target architecture from a general sparse matrix representation. However libraries have limited composability, address very specific optimization strategies, and have to be rewritten as new architectures emerge. In this dissertation, we explore the use of the inspector/executor methodology to accomplish the code and data transformations to tailor high performance sparse matrix representations. We devise and embed abstractions for such inspector/executor transformations within a compiler framework so that they can be composed with a rich set of existing polyhedral compiler transformations to derive complex transformation sequences for high performance. We demonstrate the automatic generation of inspector/executor code, which orchestrates code and data transformations to derive high performance representations for the Sparse Matrix Vector Multiply kernel in particular. We also show how the same transformations may be integrated into sparse matrix and graph applications such as Sparse Matrix Matrix Multiply and Stochastic Gradient Descent, respectively. The specific constraints of these applications, such as problem size and dependence structure, necessitate unique sparse matrix representations that can be realized using our transformations. Computations such as Gauss Seidel, with loop carried dependences at the outer most loop necessitate different strategies for high performance. Specifically, we organize the computation into level sets or wavefronts of irregular size, such that iterations of a wavefront may be scheduled in parallel but different wavefronts have to be synchronized. We demonstrate automatic code generation of high performance inspectors that do explicit dependence testing and level set construction at runtime, as well as high performance executors, which are the actual parallelized computations. For the above sparse matrix applications, we automatically generate inspector/executor code comparable in performance to manually tuned libraries

Semi-random Graphs with Planted Sparse Vertex Cuts: Algorithms for Exact and Approximate Recovery

The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a O(sqrt{log n})-approximation algorithm due to Feige et al. [Uriel Feige et al., 2008], and O(sqrt{OPT log d}) bound in graphs having vertex degrees at most d due to Louis et al. [Louis et al., 2013]. We study a natural semi-random model of graphs with sparse vertex cuts. For certain ranges of parameters, we give an algorithm to recover the planted sparse vertex cut exactly. For a larger range of parameters, we give a constant factor bi-criteria approximation algorithm to compute the graph\u27s balanced vertex expansion. Our algorithms are based on studying a semidefinite programming relaxation for the balanced vertex expansion of the graph. In addition to being a family of instances that will help us to better understand the complexity of the computation of vertex expansion, our model can also be used in the study of community detection where only a few nodes from each community interact with nodes from other communities. There has been a lot of work on studying random and semi-random graphs with planted sparse edge cuts. To the best of our knowledge, our model of semi-random graphs with planted sparse vertex cuts has not been studied before

Tight SoS-Degree Bounds for Approximate Nash Equilibria

Nash equilibria always exist, but are widely conjectured to require time to find that is exponential in the number of strategies, even for two-player games. By contrast, a simple quasi-polynomial time algorithm, due to Lipton, Markakis and Mehta (LMM), can find approximate Nash equilibria, in which no player can improve their utility by more than ε by changing their strategy. The LMM algorithm can also be used to find an approximate Nash equilibrium with near-maximal total welfare. Matching hardness results for this optimization problem were found assuming the hardness of the planted-clique problem (by Hazan and Krauthgamer) and assuming the Exponential Time Hypothesis (by Braverman, Ko and Weinstein). In this paper we consider the application of the sum-squares (SoS) algorithm from convex optimization to the problem of optimizing over Nash equilibria. We show the first unconditional lower bounds on the number of levels of SoS needed to achieve a constant factor approximation to this problem. While it may seem that Nash equilibria do not naturally lend themselves to convex optimization, we also describe a simple LP (linear programming) hierarchy that can find an approximate Nash equilibrium in time comparable to that of the LMM algorithm, although neither algorithm is obviously a generalization of the other. This LP can be viewed as arising from the SoS algorithm at log n levels – matching our lower bounds. The lower bounds involve a modification of the Braverman-Ko-Weinstein embedding of CSPs into strategic games and techniques from sum-of-squares proof systems. The upper bound (i.e. analysis of the LP) uses information-theory techniques that have been recently applied to other linear- and semidefinite programming hierarchies

INSULIN SECRETAGOGUE EFFECT OF ROOTS OF RAVENALA MADAGASCARIENSIS SONN. - AN IN VITRO STUDY

Objective: The objective of this study was to establish the cytotoxicity profile and to evaluate the insulin secretagogue effect of ethanolic root extract of Ravenala madagascariensis Sonn. Methods: The cell viability of rat insulinoma 5F (RIN5F) cell lines over the treatment of plant extract was assessed by 3-(4,5-dimethyl-2-thiazolyl)- 2,5-diphenyltetrazolium bromide assay. The insulin-releasing effect was evaluated by insulin secretion assay over RIN5F cell lines by enzyme-linked immunosorbent assay. Results: The ethanolic extract of the roots of R. madagascariensis Sonn. showed negligible cytotoxicity at 20–40 μg/ml, and hence, concentrations up to 40 μg/ml were used in insulin secretion assay. The ethanolic root extract at 20 and 40 μg/ml significantly (p<0.05 compared to control) stimulated the insulin release in a dose-dependent manner even in the presence of glucose at lower and higher concentrations (5 and 10 mM). Conclusion: Thus, our results validate its traditional claim in the treatment of diabetes by stimulating the secretion of insulin, thereby suggesting a possible mechanism of its antidiabetic effect

MISIM: A Novel Code Similarity System

Code similarity systems are integral to a range of applications from code recommendation to automated software defect correction. We argue that code similarity is now a first-order problem that must be solved. To begin to address this, we present machine Inferred Code Similarity (MISIM), a novel end-to-end code similarity system that consists of two core components. First, MISIM uses a novel context-aware semantic structure, which is designed to aid in lifting semantic meaning from code syntax. Second, MISIM provides a neural-based code similarity scoring algorithm, which can be implemented with various neural network architectures with learned parameters. We compare MISIM to three state-of-the-art code similarity systems: (i) code2vec, (ii) Neural Code Comprehension, and (iii) Aroma. In our experimental evaluation across 328,155 programs (over 18 million lines of code), MISIM has 1.5x to 43.4x better accuracy than all three systems