8360631
Kinetic Connectivity for Unit Disks
We describe a kinetic data structure (KDS) that maintains the connected components of the union of a set of unit-radius disks moving in the plane. We assume that the motion of each disk can be specified by a low-degree algebraic trajectory; this trajectory, however, can be modified in an on-line fashion. While the disks move continuously, their connectivity changes at discrete times. Our main result is an O(n) space data structure that takes O(log  n\slash \kern -1pt log log  n) time per connectivity query of the form ``are disks A and B in the same connected component?’’ A straightforward approach based on dynamically maintaining the overlap graph requires Ω (n2) space. Our data structure requires only linear space and must deal with O(n2 + ε) updates in the worst case, each requiring O(log 2 n) amortized time, for any ε>0 . This number of updates is close to optimal, since a set of n moving unit disks can undergo Ω (n2) connectivity changes.
100573
A hierarchical method for real-time distance computation among moving convex bodies
Abstract This paper presents the Hierarchical Walk , or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. For convex polygons, we prove that H-Walk improves on the classic Lin–Canny and Dobkin–Kirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. Experimental results indicate that, unlike previous incremental distance computation algorithms, H-Walk adapts well to variable coherence in the motion and provides consistent performance.
591702
Compact Voronoi Diagrams for Moving Convex Polygons
We describe a kinetic data structure for maintaining a compact Voronoi-like diagram of convex polygons moving around in the plane. We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96]. A key feature of this diagram is that its size is only a function of the number of polygons and not of their complexity. We demonstrate a local certifying property of that diagram, akin to that of Delaunay triangulations of points. We then obtain a method for maintaining this diagram that is output-sensitive and costs O(log n) per update. Furthermore, we show that for a set of k polygons with a total of n vertices moving along bounded degree algebraic motions, this dual diagram, and thus their compact Voronoi diagram, changes combinatorially Ω(n2) and O(kn2β(k)β(n)) times, where β(ċ) is an extremely slowly growing function. This compact Voronoi diagram can be used for collision detection or retraction motion planning among the moving polygons.
9035359
Visibility Queries in Simple Polygons and Applications
In this paper we explore some novel aspects of visibility for stationary and moving points inside a simple polygon P. We provide a mechanism for expressing the visibility polygon from a point as the disjoint union of logarithmically many canonical pieces using a quadraticspace data structure. This allows us to report visibility polygons in time proportional to their size, but without the cubic space overhead of earlier methods. The same canonical decomposition can be used to determine visibility within a frustum, or to compute various attributes of the visibility polygon efficiently. By exploring the connection between visibility polygons and shortest path trees, we obtain a kinetic algorithm that can track the visibility polygon as the viewpoint moves along polygonal paths inside P, at a polylogarithmic cost per combinatorial change in the visibility. The combination of the static and kinetic algorithms leads to a space query-time tradeoff for the visibility from a point problem and an output-sensitive algorithm for the weak visibility from a segment problem.
11907465
Deformable Free-Space Tilings for Kinetic Collision Detection†
We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously. Unlike classical collision detection methods that rely on bounding volume hierarchies, our method is based on deformable tilings of the free space surrounding the polygons. The basic shape of our tiles is that of a pseudo-triangle, a shape sufficiently flexible to allow extensive deformation, yet structured enough to make detection of self-collisions easy. We show different schemes for maintaining pseudo-triangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that the pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. In addition, by refining the pseudo-triangulation, we show triangulations of points that only change about O(n 7 / 3 ) times for linear motion. We then describe an algorithm for maintaining a pseudo-triangulation of a set of convex polygons. Finally, we extend our algorithm to the general case of maintaining a pseudo-triangulation of a set of moving or deforming simple polygons.
15556637
Proximity problems on moving points
A kinetic data structure for the maintenance of a multidimensional range search tree is introduced. This structure is used as a building block to obtain kinetic data structures for two classical geometric proximity problems in arbitrary dlmensions: the first structure maintains the closest pair of a set of continuously moving points, and is provably efficient. The second structure maintains a spanning tree of the moving points whose cost remains within some prescribed factor of the minimum spanning tree.
18035076
On Subsumption Removal and On-the-Fly CNF Simplification
CNF Boolean formulas generated from resolution or solution enumeration often have much redundancy. Efficient algorithms are needed to simplify and compact such CNF formulas. In this paper, we present a novel algorithm to maintain a subsumption-free CNF clause database by efficiently detecting and removing subsumption as the clauses are being added. We then present an algorithm that compact CNF formula further by applying resolutions to make it Decremental Resolution Free. Our experimental evaluations show that these algorithms are efficient and effective in practice.
32889588
Enhanced visualization of time series through higher fourier harmonics
Visualization techniques can enable the exploration and detection of patterns and relationships in a complex data set by presenting the data in a graphical format in which the key characteristics become more apparent. A new visualization technique, the first Fourier harmonic projection (FFHP) was introduced to translate the multi-dimensional data into a two dimensional scatter plot where the spatial relationship of the points reflects the structure of the original data set. FFHP has been shown capable of visualizing various gene expression data sets. However, dimension arrangement is crucial for the effectiveness of FFHP and certain data, such as time series, prevents dimensions (time points) from being freely rearranged. In this paper, we present an alternative approach through higher Fourier harmonic projections to enhance the visualization. Our algorithm takes advantage of the theoretical meaning of the Fourier harmonics and "reshuffles" the dimensions of the data set without physically rearranging them. The experimental results demonstrated significant improvement of the visualizations.
15318356
Variance estimation over sliding windows
Capturing characteristics of large data streams has received considerable attention. The constraints in space and time restrict the data stream processing to only one pass (or a small number of passes). Processing data streams over sliding windows make the problem more difficult and challenging. In this paper, we address the problem of maintaining ∈-approximate variance of data streams over sliding windows. To our knowledge, the best existing algorithm requires O(1/∈2 log N) space, though the lower bound for this problem is Ω(1/∈ log N). We propose the first ∈-approximation algorithm to this problem that is optimal in both space and worst case time. Our algorithm requires O(1/∈ log N) space. Furthermore, its running time is O(1) in worst case.
18758619
IGroup: a web image search engine with semantic clustering of search results
In this demo, we present IGroup, a Web image search engine that organizes the search results into semantic clusters. Different from all existing Web image search results clustering algorithms that only cluster the top few images using visual or textual features, IGroup first identifies several query-related semantic clusters based on a key phrases extraction algorithm originally proposed for clustering general Web search results. Then, all the resulting images are separated and assigned to corresponding clusters. To make the best use of the clustering results, a new user interface is proposed. Please go to http://igroup.msra.cn for real experience.
38635352
A neural network based classifier for handwritten Chinese character recognition
In this paper, a geometrical approach for building neural networks is proposed. With the proposed approach, it is very easy to construct an efficient neural classifier to solve the handwritten Chinese character recognition problem, as well as other pattern recognition problems of large scale. Experiments are conducted to evaluate the performance of the proposed approach and results obtained are promising.