2273352
Near-Linear Time Approximation Algorithms for Curve Simplification
AbstractWe consider the problem of approximating a polygonal
 curve P under a given error criterion by another
 polygonal curve P’ whose vertices are a
 subset of the vertices of P. The goal is to minimize
 the number of vertices of P’ while ensuring that the
 error between P’ and P is below a certain threshold.
 We consider two different error measures: 
 Hausdorff and Frechet. For both error criteria, we present
 near-linear time approximation algorithms that, given a
 parameter ε > 0, compute a simplified polygonal
 curve P’ whose error is less than ε and
 size at most the size of an optimal simplified
 polygonal curve with error ε/2. We consider
 monotone curves in ℝ2 in the case of the Hausdorff error measure
 under the uniform distance metric
 and arbitrary curves in any dimension for the Frechet error measure
 under Lp metrics. 
 We present
 experimental results demonstrating that our algorithms
 are simple and fast, and produce close to optimal
 simplifications in practice.
12092202
Box-trees and R-trees with near-optimal query time
A box-tree is a \ifasci so-called \emph{bounding-volume hierarchy} \else bounding-volume hierarchy \fi that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.
14111088
I/O-efficient dynamic point location in monotone planar subdivisions
We present an efficient external-memory dynamic data structure for point location in monotone planar subdivisions. Our data structure uses O(N/B) disk blocks to store a monotone subdivision of size N, where B is the size of a disk block. It supports queries in O(logi N) I/OS (worst-case) and updates in O(lo& N) I/OS (amortized). We also propose a new variant of B-trees, called leuelbalanced B-trees, which allow insert, delete, merge, and split operations in O((l+ $ logM,B f) log, N) I/OS (amortized), 2 5 b 2 B/2, even if each node stores a pointer to its parent. Here M is the size of main memory. Besides being essential to our point-location data structure, we believe that level-balanced B-trees are of significant independent interest. They can, for example, be used to dynamically maintain a planar St-graph using O((1 + $10g~,~ $$) log, N) = O(logi N) I/OS (amortized) per update, so that reachability queries can be answered in O(log, N) I/OS (worst case).
206566847
Circle Shooting in a Simple Polygon
Consider the following problem: Given a simple n-gon P, preprocess it so that for a query circle π and a point s on π, one can quickly compute Φ(P, π, s), the first intersection point between P and π as we follow π from s in clockwise direction. We show that P can be preprocessed, in time O(n log3n), into a data structure of size O(n log3n), so that, for a query circle π, Φ(P, π, s) can be computed in O(log4n) time. We apply the circle shooting algorithm to report all K intersections between a set of m circular arcs and another set of n circular arcs in time O((m√n + n√m )log2.5(m + n) + (K + m + n)log4(m + n)).
20881960
On the complexity of many faces in arrangements of circles
We obtain improved bounds on the complexity of m distinct faces in an arrangement of n circles and in an arrangement of n unit circles. The bounds are worst-case tight for unit circles, and, for general circles, they nearly coincide with the best known bounds for the number of incidences between m points and n circles.
70446
An optimal dynamic interval stabbing-max data structure?
In this paper we consider the dynamic stabbing-max problem, that is, the problem of dynamically maintaining a set <i>S</i> of <i>n</i> axis-parallel hyper-rectangles in R<sup><i>d</i></sup>, where each rectangle <i>s</i> ∈ <i>S</i> has a weight <i>w</i>(<i>s</i>) ∈ R, so that the rectangle with the maximum weight containing a query point can be determined efficiently. We develop a linear-size structure for the one-dimensional version of the problem, the <i>interval stabbing-max</i> problem, that answers queries in worst-case <i>O</i>(log <i>n</i>) time and supports updates in amortized <i>O</i>(log <i>n</i>) time. Our structure works in the pointer-machine model of computation and utilizes many ingredients from recently developed external memory structures. Using standard techniques, our one-dimensional structure can be extended to higher dimensions, while paying a logarithmic factor in space, update time, and query time per dimension. Furthermore, our structure can easily be adapted to external memory, where we obtain a linear-size structure that answers queries and supports updates in <i>O</i>(log<inf><i>B</i></inf> <i>n</i>) I/Os, where <i>B</i> is the disk block size.
16920879
A Pragmatic Solution to an Indian Accented English Speech Synthesizer Using Residual Excited Linear Predictive Coded Voice
This paper elucidates a practical solution to an Indian accented English text to speech synthesizing system. The paper covers the complete procedure to generate the speech signal of the text, in Indian accented voice. The technique described considers the various prosodic features that need to be incorporated into the synthesized speech to make it appear natural and in the way an Indian speaks. The paper describes the complete method for synthesizing the speech including the pre-processing of the text and prosody analysis in the Indian style of speaking. The diphones extracted from an Indian’s voice are coded using Residual Excited Linear Predictive (RELP) coding technique and the resulting formants and residual values of the diphones are used to resynthesize the final output speech for the text to be synthesized. ‘PALSA’ – an Indian accented English speech synthesizer has been successfully implemented using the mentioned technique to produce the Indian accented speech and is described in this paper.