Guth [13] showed that given a family S of n g-dimensional semi-algebraic sets in R d and an integer parameter D ≥ 1, there is a d-variate partitioning polynomial P of degree at most D, so that each connected component of R d \ Z(P ) intersects O(n/D d−g ) sets from S. Such a polynomial is called a generalized partitioning polynomial. We present a randomized algorithm that efficiently computes such a polynomial P . Specifically, the expected running time of our algorithm is only linear in |S|, where the constant of proportionality depends on d, D, and the complexity of the description of S. Our approach exploits the technique of quantifier elimination combined with that of ε-samples.We present four applications of our result. The first is a data structure for answering pointlocation queries among a family of semi-algebraic sets in R d in O(log n) time; the second is data structure for answering range search queries with semi-algebraic ranges in O(log n) time; the third is a data structure for answering vertical ray-shooting queries among semi-algebraic sets in R d in O(log 2 n) time; and the fourth is an efficient algorithm for cutting algebraic planar curves into pseudo-segments, i.e., into Jordan arcs, each pair of which intersect at most once.

In contrast to developed countries, Indian capital markets do not exhibit strong efficiency and therefore it appears possible that fund managers beat the benchmarks. We examine the existence of superior performance of open-ended equity mutual funds in India with various models including traditional Capital Asset Pricing Model (CAPM)-based as well as recent Fama–French–Carhart (FFC)-factors-based models. We use a survivorship-bias free database including all schemes since inception till recently. We found evidence of stock picking and timing abilities in Indian fund managers. Our results are robust to changes in benchmarks, return frequency, and effects of heteroscedasticity and autocorrelation (HAC).

We develop (single-pass) streaming algorithms for maintaining extent measures of a stream S of n points in R d . We focus on designing streaming algorithms whose working space is polynomial in d (poly(d)) and sublinear in n. For the problems of computing diameter, width and minimum enclosing ball of S, we obtain lower bounds on the worst-case approximation ratio of any streaming algorithm that uses poly(d) space. On the positive side, we introduce the notion of blurred ball cover and use it for answering approximate farthestpoint queries and maintaining approximate minimum enclosing ball and diameter of S. We describe a streaming algorithm for maintaining a blurred ball cover whose working space is linear in d and independent of n.

No abstract