570803
Provable dimension detection using principal component analysis
We present simple algorithms for detecting the dimension k of a smooth manifold M ⊂ Rd from a set P of point samples, provided that P satisfies a standard sampling condition as in previous results. The best running time so far is O(d2O(k7 log k)) worst-case by Giesen and Wagner after the adaptive neighborhood graph is constructed in O(d|P|2) worst-case time. Given the adaptive neighborhood graph, for any l ≥ 1, our algorithm outputs the true dimension with probability at least 1-2-l in O(2O(k)kd(k + l log d)) expected time. Our experimental results validate the effectiveness of our approach in computing the dimension. A further advantage is that both the algorithm and its analysis can be generalized to the noisy case, in which outliers and a small perturbation of the samples are allowed.
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)).
18478207
Prefix-Free Regular-Expression Matching
We explore the regular-expression matching problem with respect to prefix-freeness of the pattern. We show that the prefix-free regular expression gives only linear number of matching substrings in the size of a given text. Based on this observation, we propose an efficient algorithm for the prefix-free regular-expression matching problem. Furthermore, we suggest an algorithm to determine whether or not a given regular language is prefix-free.
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.
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 ...
2134196
Counting Structures in Grid Graphs, Cylinders and Tori Using Transfer Matrices: Survey and New Results
There is a very large literature devoted to counting structures, e.g., spanning trees, Hamiltonian cycles, independent sets, acyclic orientations, in the n×m grid graph G(n,m). In particular the problem of counting the number of structures in fixed height graphs, i.e., fixing m and letting n grow, has been, for different types of structures, attacked independently by many different authors, using a transfer matrix approach. This approach essentially permits showing that the number of structures in G(n,m) satisfies a fixed-degree constant-coefficient recurrence relation in n. In contrast there has been surprisingly little work done on counting structures in grid-cylinders (where the left and right, or top and bottom, boundaries of the grid are wrapped around and connected to each other) or in grid-tori (where the left edge of the grid is connected to the right and the top edge is connected to the bottom one). The goal of this paper is to demonstrate that, with some minor modifications, the transfer matrix technique can also be easily used to count structures in fixed height grid-cylinders and tori.
23798301
The cognitive process of comprehension
Comprehension is the action or capability of understanding. Comprehension is a higher cognitive process of the brain that searches relations between a given object or attribute and other objects, attributes, and relations in the long-term memory, and establishes a representational model for the object or attribute by connecting it to appropriate clusters of memory. It is recognized that although knowledge and information are powerful, before any information can be possessed and processed, it should be comprehended properly. This paper intends to model one of the cognitive life functions, comprehension, in cognitive informatics. The mechanism and process of comprehension are described based on the cognitive model of the brain developed by Wang. Then, real-time process algebra (RTPA) is used to formally describe the comprehension process.
7211983
Theoretical Analysis for Communication-Induced Checkpointing Protocols with Rollback-Dependency Trackability
Rollback-Dependency Trackability (RDT) is a property that states that all rollback dependencies between local checkpoints are on-line trackable by using a transitive dependency vector. In this paper, we address three fundamental issues in the design of communication-induced checkpointing protocols that ensure RDT. First, we prove that the following intuition commonly assumed in the literature is in fact false: If a protocol forces a checkpoint only at a stronger condition, then it must take, at most, as many forced checkpoints as a protocol based on a weaker condition. This result implies that the common approach of sharpening the checkpoint-inducing condition by piggybacking more control information on each message may not always yield a more efficient protocol. Next, we prove that there is no optimal on-line RDT protocol that takes fewer forced checkpoints than any other RDT protocol for all possible communication patterns. Finally, since comparing checkpoint-inducing conditions is not sufficient for comparing protocol performance, we present some formal techniques for comparing the performance of several existing RDT protocols.
21757365
Estimating coronary artery lumen area with optimization-based contour detection
A modified optimization-based contour detection method was presented to compute the lumen area of the coronary artery from intravascular ultrasound (IVUS) video images. First, the search range for the artery inner wall was determined based on the continuity of IVUS video frames. Next, the internal and external energy were calculated to describe the smoothness of the arterial wall and the grayscale variation of ultrasound images, respectively. Here, a novel form of the external energy which combines the gradient and variance of the intensity of image in the radial direction was used. Finally, the minimal energy path based on the optimum contour of the artery wall was obtained using circular dynamic programming (DP). By the comparison with the typical DP procedure using the traditional external energy form, based only on the image gradient, the reliability of this modified method is considerably improved in the measurement of coronary artery lumen area.
7748348
Shape fitting with outliers
Given a set <i>H</i> of <i>n</i> hyperplanes in <i>R<sup>d</sup></i>, we present an algorithm that <i>e</i>-approximates the extent between the top and bottom <i>k</i> levels of the arrangement of <i>H</i> in time <i>O(n + (k/e)<sup>c</sup>)</i>, where <i>c</i> is a constant depending on <i>d</i>. The algorithm relies on computing a subset of <i>H</i> of size.<i>O(k/e<sup>d-1</sup>)</i>, in near linear time, such that the <i>k</i>-level of the arrangement of the subset approximates that of the original arrangement. Using this algorithm, we propose efficient approximation algorithms for shape fitting with outliers for various shapes. This is the first algorithms to handle outliers efficiently for the shape fitting problems considered.
2472095
Coarse and Reliable Geometric Alignment for Protein Docking
We present an efficient algorithm for generating a small set of coarse alignments between interacting proteins using meaningful features on their surfaces. The proteins are treated as rigid bodies, but the results are more generally useful as the produced configurations can serve as input to local improvement algorithms that allow for protein flexibility. We apply our algorithm to a diverse set of protein complexes from the Protein Data Bank, demonstrating the effectivity of our algorithm, both for bound and for unbound protein docking problems.