17134961
A Near-Quadratic Algorithm for Fence Design
A part feeder is a mechanism that receives a stream of identical parts in arbitrary orientations and outputs them oriented the same way. Various sensorless part feeders have been proposed in the literature. The feeder we consider consists of a sequence of fences that extend partway across a conveyor belt; a polygonal part P carried by the belt is reoriented by each fence it encounters. We present an O(m + n2 log3n)-time algorithm to compute a sequence of fences that uniquely orients P, if one exists, where m is the total number of vertices and n is the number of stable edges of P. We reduce the problem to searching for a path in a state graph that has O(n3) edges. By exploiting various geometric properties of this graph, we show that it can be represented implicitly and that a desired path can be computed in O(m + n2 log3n) time. We believe that our technique is quite general and could be applicable to other part-manipulation problems as well.
1016609
A 2D kinetic triangulation with near-quadratic topological changes
A triangulation of a set <i>S</i> of points in the plane is a subdivision of the convex hull of <i>S</i> into triangles whose vertices are points of <i>S</i>. Given a set <i>S</i> of <i>n</i> points in ℝ<sup>3</sup>, each moving independently, we wish to maintain a triangulation of S. The triangulation needs to be updated periodically as the points in <i>S</i> move, so the goal is to maintain a triangulation with small number of topological events, each being the insertion or deletion of an edge. We propose a kinetic data structure (KDS) that processes n<sup>2</sup> 2<sup>O(√log n•log log n )</sup> topological events, with high probability, if the trajectories of input points are algebraic curves of fixed degree. Each topological event can be processed in <i>O</i>(log <i>n</i>) time. This is the first known KDS for maintaining a triangulation that processes near-quadratic number of topological events, and almost matches the Ω(<i>n</i><sup>2</sup>) lower bound, [1]. The number of topological events can be reduced to nk • 2<sup>O(√log k•log log n )</sup> if only <i>K</i> of the points are moving.
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.
9832346
Computing envelopes in four dimensions with applications
Let <inline-equation> <f> <sc>F</sc></f> </inline-equation> be a collection of n d-variate, possibly partially defined, functions, all algebraic of some constant maximum degree. We present a randomized algorithm that computes the vertices, edges, and 2-faces of the lower envelope (i.e., pointwise minimum) of <inline-equation> <f> <sc>F</sc></f>  </inline-equation> in expected time O(n<supscrpt>d+ε</supscrpt>), for any ε>0. For d=3, by combining this algorithm with the point location technique of Preparata and Tamassia, we can compute, in randomized expected time O(n<supscrpt>3+ε</supscrpt>) for any ε>0, a data structure of size O(n<supscrpt>3+ε</supscrpt>) that, given any query point q, can determine in O(log<supscrpt>2</supscrpt>n) time whether q lies above, below or on the envelope. As a consequence, we obtain improved algorithmic solutions to many problems in computational geometry, including (a) computing the width of a point set in 3-space, (b) computing the biggest stick in a simple polygon in the plane, and (c) computing the smallest-width annulus covering a planar point set. The solutions to these problems run in time O(n<supscrpt>17/11+ε</supscrpt>), for any ε>0 improving previous solutions that run in time O(n<supscrpt>8/5+ε</supscrpt>). We also present data structures for (i) performing nearest-neighbor and related queries for fairly general collections of objects in 3-space and for collections of moving objects in the plane, and (ii) performing ray-shooting and related queries among n spheres or more general objects in 3-space. Both of these data structures require O(n<supscrpt>3+ε</supscrpt>) storage and preprocessing time, for any ε>0, and support polylogarithmic-time queries. These structures improve previous solutions to these problems.
14529095
Approximating Shortest Paths on a Nonconvex Polyhedron
We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in ${\mathbb R}^3$ and two points s and t on P, constructs a path on P between s and t whose length is at most ${7(1+{\varepsilon})} dP(s,t), where dP(s,t) is the length of the shortest path between s and t on P, and ${\varepsilon} > 0$ is an arbitrarily small positive constant. The algorithm runs in O(n5/3 log5/3 n) time, where n is the number of vertices in P. We also present a slightly faster algorithm that runs in O(n8/5 log8/5 n) time and returns a path whose length is at most ${15(1+{\varepsilon})} d_{P}(s,t)$.
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.
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.