1333188
Querying approximate shortest paths in anisotropic regions
We present a data structure for answering approximate shortest path queries ina planar subdivision from a fixed source. Let ρ ≥ 1 be a real number.Distances in each face of this subdivision are measured by a possiblyasymmetric convex distance function whose unit disk is contained in aconcentric unit Euclidean disk, and contains a concentric Euclidean disk withradius 1/ρ. Different convex distance functions may be used for differentfaces, and obstacles are allowed. Let ε be any number strictly between 0and 1. Our data structure returns a (1+ε)approximation of the shortest path cost from the fixed source to a querydestination in O(logρn/ε) time. Afterwards, a(1+ε)-approximate shortest path can be reported in time linear in itscomplexity. The data structure uses O(ρ<sup>2</sup> n<sup>4</sup>/ε<sup>2</sup> log ρn/ε) space and can be built in O((ρ<sup>2</sup> n<sup>4</sup>)/(ε<sup>2</sup>)(log ρn/ε)<sup>2</sup>) time. Our time and space bounds do not depend onany geometric parameter of the subdivision such as the minimum angle.
14088697
Approximate shortest paths in anisotropic regions
Our goal is to find an approximate shortest path for a point robot moving in a planar subdivision with <i>n</i> vertices. Let ρ ≥ 1 be a real number. Distances in each face of this subdivision are measured by a convex distance function whose unit disk is contained in a concentric unit Euclidean disk, and contains a concentric Euclidean disk with radius 1/ρ. Different convex distance functions may be used for different faces, and obstacles are allowed. These convex distance functions may be asymmetric. For all ε ∈ (0, 1), and for any two points <i>v<inf>s</inf></i> and <i>v<inf>d</inf></i>, we give an algorithm that finds a path from <i>v<inf>s</inf></i> to <i>v<inf>d</inf></i> whose cost is at most (1 + ε) times the minimum cost. Our algorithm runs in <i>O</i> (ρ<sub>2</sub>logρ/ε<sup>2</sup>n<sup>3</sup> log (ρn/ε)) time. This bound does not depend on any other parameters; in particular, it does not depend on the minimum angle in the subdivision. We give applications to two special cases that have been considered before: the weighted region problem and motion planning in the presence of uniform flows. For the weighted region problem with weights in [1, ρ] ∪ {∞}, the time bound of our algorithm improves to <i>O</i> (ρ<sub>2</sub>logρ/εn<sup>3</sup> log (ρn/ε)).
38202538
Infix-free Regular Expressions and Languages
We study infix-free regular languages. We observe the structural properties of finite-state automata for infix-free languages and develop a polynomial-time algorithm to determine infix-freeness of ...
18488788
A preference aggregation method through the estimation of utility intervals
In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method.
14953442
Estimating the Selectivity of XML Path Expression with Predicates by Histograms
Selectivity estimation of path expressions in querying XML data plays an important role in query optimization. A path expression may contain multiple branches with predicates, each of which having its impact on the selectivity of the entire query. In this paper, we propose a novel method based on 2-dimensional value histograms to estimate the selectivity of path expressions embedded with predicates. The value histograms capture the correlation between the structures and the values in the XML data. We define a set of operations on the value histograms as well as on the traditional histograms that capture nodes positional distribution. We then construct a cost tree based on such operations. The selectivity of any node (or branch) in a path expression can be estimated by executing the cost tree. Compared with previous methods (which ignore value distribution) our method offers much better estimation accuracy.
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.
9419834
A Two-Dimensional Kinetic Triangulation with Near-Quadratic Topological Changes
A triangulation of a set S of points in the plane is a subdivision of the convex hull of S into triangles whose vertices are points of S. Given a set S of n points in ${\Bbb R}^2,$ each moving independently, we wish to maintain a triangulation of S. The triangulation needs to be updated periodically as the points in S move, so the goal is to maintain a triangulation with a small number of topological events, each being the insertion or deletion of an edge. We propose a kinetic data structure (KDS) that processes $n^2 2^{O(\sqrt{\log n \cdot \log \log n})}$ topological events with high probability if the trajectories of input points are algebraic curves of fixed degree. Each topological event can be processed in $O(\log n)$ time. This is the first known KDS for maintaining a triangulation that processes a near-quadratic number of topological events, and almost matches the $\Omega(n^2)$ lower bound [1]. The number of topological events can be reduced to $nk\cdot 2^{O(\sqrt{\log k \cdot \log\log n})}$ if only k of the points are moving.
39368933
Improved QIM Strategies for Gaussian Watermarking
This paper revisits the problem of watermarking a Gaussian host, where the embedder and attacker are subject to mean-squared distortion constraints. The worst (nonadditive) attack and unconstrained capacity have been identified in previous work. Here we constrain the encoding function to lie in a given family of encoding functions — such as spread-spectrum or fixed-dimensional Quantization Index Modulation (QIM), with or without time-sharing, with or without external dithering. This gives rise to the notion of constrained capacity. Several such families are considered in this paper, and the one that is best under the worst attack is identified for each admissible value of the watermark-to-noise ratio (WNR) and the noise-to-host ratio (NHR). With suitable improvements, even scalar QIM can outperform any (improved) spread-spectrum scheme, for any value of WNR and NHR. The remaining gap to unconstrained capacity can be bridged using higher-dimensional lattice QIM.