5478794
Euclidean proximity and power diagrams
Power diagrams [Aur87] are a useful generalization of Voronoi diagrams in which the sites defining the diagram are not points but balls. They derive their name from the fact that the distance used in their definition is not the standard Euclidean distance, but instead the classical notion of the power of a point with respect to a ball [Cox61]. The advantage of the power distance is that the ‘bisector surfaces’, the surfaces equidistant from two given balls, are hyper-planes, and thus the Euclidean structure of these diagrams is polyhedral and they are easier to compute and manipulate than standard Voronoi diagrams. Several algorithms and applications for the power diagrams are already known, including those referenced in [IIM85, Aur88]. Most recently power diagrams have played a key role in work related to alpha shapes and ‘skins’ [Ede93, EM94, Ede95], as collections of balls are a natural model for molecular structures. The Voronoi diagram of point sites in any dimension has many useful proximity properties. Let us say that two sites are neighbors in the Voronoi diagram if their Voronoi cells share a common facet. It is well known that, for a set of points S, the closest pair of points in S are neighbors in the Voronoi diagram of S — equivalently, the closest pair of points must define an edge of the dual Delaunay diagram. Even more is true: the nearest neighbor to any point p ∈ S is a neighbor to p in the Voronoi diagram (equivalently, is connected to this neighbor by a Delaunay edge). Surprisingly, it seems that analogous proximity properties have not been studied for the power diagram. In this note, we consider the the power diagram of a set of disjoint balls. We show that the closest pair of
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.
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.
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.
174192
Fault tolerant networks with small degree
In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph <italic>G</italic> (linear array or mesh in this paper), a graph <italic>G</italic>′ is called a &kgr;-fault-tolerant graph of <italic>G</italic> if when we remove any &kgr; nodes from <italic>G</italic>′, it still contains a subgraph isomorphic to <italic>G</italic>. The major quality measures for a fault-tolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree <italic>O</italic>(1) for arrays and <italic>O</italic>(log<supscrpt>3</supscrpt> &kgr;) for meshes. The number of spare nodes used are <italic>O</italic>(&kgr; log<supscrpt>2</supscrpt> &kgr;) and <italic>O</italic>(&kgr;<supscrpt>2</supscrpt>/log &kgr;), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in &kgr;.
3730862
Distributed Resource Allocation in Stream Processing Systems
Distributed stream processing architecture has emerged as appealing solution to coping with the analysis of large amount of data from dispersed sources. A fundamental problem in such stream processing systems is how to best utilize the available resources so that the overall system performance is optimized. We consider a distributed stream processing system that consists of a network of cooperating servers, collectively providing processing services for multiple data streams. Each stream is required to complete a series of operations on various servers. We assume all servers have finite computing resources and all communication links have finite available bandwidth. The problem is to find distributed schemes to allocate the limited computing resources as well as the communication bandwidth in the system so as to achieve a maximum concurrent throughput for all output streams. We present a generalized multicommodity flow model for the above problem. We develop a distributed resource allocation algorithm that guarantees the optimality. We also provide detailed analysis on the complexity of the algorithm and demonstrate the performance using numerical experiments.
11528752
Redundancy in Complete Sets
We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaser et al. [12], complete sets for all of the following complexity classes are m-mitotic: NP, coNP, $\bigoplus$P, PSPACE, and NEXP, as well as all levels of PH, MODPH, and the Boolean hierarchy over NP. In the cases of NP, PSPACE, NEXP, and PH, this at once answers several well-studied open questions. These results tell us that complete sets share a redundancy that was not known before. In particular, every NP-complete set A splits into two NP-complete sets A1 and A2.
16393711
Salient Feature Selection for Visual Concept Learning
Image classification could be treated as an effective solution to enable keyword-based semantic image retrieval. In this paper, we propose a novel image classification framework by learning semantic concepts of image categories. To choose representative features for an image category and meanwhile reduce noisy features, a three-step salient feature selection strategy is proposed. In the feature selection stage, salient patches are first detected and clustered. Then the region of dominance and salient entropy measures are calculated to reduce non-common salient patches for the category. Based on the selected visual keywords, SVM and keyword frequency model categorization method are applied to classification, respectively. The experimental results on Corel image database demonstrate that the proposed salient feature selection approach is very effective in image classification and visual concept learning.
6040398
C-DIST: efficient distance computation for rigid and articulated models in configuration space
The problem of distance computation arises in many applications including motion planning, CAD/CAM, dynamic simulation and virtual environments. Most prior work in this area has been restricted to separation or penetration distance computation between two objects. In this paper, we address the problem of computing a measure of distance between two configurations of a rigid or articulated model. The underlying distance metric is defined as the length of the longest displacement vector over the corresponding vertices of the model between two configurations. Our algorithm is based on Chasles theorem in Screw theory, and we show that the maximum distance can be realized only by a vertex of the convex hull of a rigid object. We use this formulation to compute the distance, and present two acceleration techniques to speed up the computation: incremental walking on the dual space of the convex hull and culling vertices on the convex hull using a bounding volume hierarchy (BVH). Our algorithm can be easily extended to articulated models by maximizing the distance over its each link and we also present culling techniques to accelerate the computation. We highlight the performance of our algorithm on many complex models and describe its application to proximity queries and motion planning.
36776709
XML-based Advanced UDDI Search Mechanism for B2B Integration