B. V. Raghavendra Rao

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Functions in arithmetic NC are known to have equivalent constant width polynomial degree circuits, but the converse containment is unknown. In a partial answer to this question, we show that syntactic multilinear circuits of constant width and polynomial degree can be depth-reduced, though the resulting circuits need not be syntactic multilinear. We then(More)
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. In order to explain this performance, we develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems. Our framework can be(More)
Christofides’ algorithm is a well known approximation algorithm for the metric travelling salesman problem. As a first step towards obtaining an average case analysis of Christofides’ algorithm, we provide a probabilistic analysis for the stochastic version of the algorithm for the Euclidean traveling salesman problem, where the input consists of n randomly(More)
Given an input graph G and an integer k, the k-PATH problem asks whether there exists a path of length k in G. The counting version of the problem, #k-PATH asks to find the number of paths of length k in G. Recently, there has been a lot of work on finding and counting k-sized paths in an input graph. The current fastest (randomized) algorithm for k-PATH(More)
We study structural properties of restricted width arithmetical circuits. It is shown that syntactically multilinear arithmetical circuits of constant width can be efficiently simulated by syntactically multilinear algebraic branching programs of constant width, i.e. that sm-VSC ⊆ sm-VBWBP. Also, we obtain a direct characteriztion of poly-size arithmetical(More)
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of random metric instances for optimization problems obtained as follows: Every edge of a complete graph gets a weight drawn(More)
In the uniform circuit model of computation, the width of a boolean circuit exactly characterizes the “space” complexity of the computed function. Looking for a similar relationship in Valiant’s algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. In the uniform setting, we show that our definition(More)
The class of polynomials computable by polynomial size log-depth arithmetic circuits (VNC 1) is known to be computable by constant width polynomial degree circuits (VsSC 0), but whether the converse containment holds is an open problem. As a partial answer to this question, we give a construction which shows that syntactically multilinear circuits of(More)