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- Meena Mahajan, B. V. Raghavendra Rao
- Electronic Colloquium on Computational Complexity
- 2008

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)

- Markus Bläser, Bodo Manthey, B. V. Raghavendra Rao
- Algorithmica
- 2011

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)

- Meena Mahajan, B. V. Raghavendra Rao
- FCT
- 2009

In the uniform circuit model of computation, the width of a boolean circuit exactly characterises 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. We introduce the class VL as an algebraic variant of… (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)

- Nutan Limaye, Meena Mahajan, B. V. Raghavendra Rao
- STACS
- 2007

The parallel complexity class NC has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. [CMTV98] considered arithmetizations of two of these classes, #NC and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs… (More)

- Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, B. V. Raghavendra Rao, Saket Saurabh
- J. Comput. Syst. Sci.
- 2012

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)

- Karl Bringmann, Christian Engels, Bodo Manthey, B. V. Raghavendra Rao
- Algorithmica
- 2013

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)

- Meena Mahajan, B. V. Raghavendra Rao
- computational complexity
- 2011

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)

- Maurice J. Jansen, Meena Mahajan, B. V. Raghavendra Rao
- computational complexity
- 2013

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)