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.
5430292
A practical evaluation of kinetic data structures
In many applications of computational geometry to modeling objects and processes in the physical world, the participating objects are in a state of continuous change. Motion is the most ubiquitous kind of continuous transformation but others, such as shape deformation, are also possible. In a recent paper, Baech, Guibas, and Hershberger [BGH97] proposed the framework of kinetic data structures (KDSS) as a way to maintain, in a completely on-line fashion, desirable information about the state of a geometric system in continuous motion or change. They gave examples of kinetic data structures for the maximum of a set of (changing) numbers, and for the convex hull and closest pair of a set of (moving) points in the plane. The KDS frameworkallowseach object to change its motion at will according to interactions with other moving objects, the environment, etc. We implemented the KDSSdescribed in [BGH97],es well as came alternative methods serving the same purpose, as a way to validate the kinetic data structures framework in practice. In this note, we report some preliminary results on the maintenance of the convex hull, describe the experimental setup, compare three alternative methods, discuss the value of the measures of quality for KDSS proposed by [BGH97],and highlight some important numerical issues.
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.
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.
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;.
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.
9614158
Edge choosability of planar graphs without small cycles
Abstract We investigate structural properties of planar graphs without triangles or without 4-cycles, and show that every triangle-free planar graph G is edge-( Δ ( G )+1)-choosable and that every planar graph with Δ ( G )≠5 and without 4-cycles is also edge-( Δ ( G )+1)-choosable.
9760560
An edge-guided image interpolation algorithm via directional filtering and data fusion
Preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high-resolution image from a low-resolution counterpart. We propose a new edge-guided nonlinear interpolation technique through directional filtering and data fusion. For a pixel to be interpolated, two observation sets are defined in two orthogonal directions, and each set produces an estimate of the pixel value. These directional estimates, modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square-error estimation (LMMSE) technique into a more robust estimate, using the statistics of the two observation sets. We also present a simplified version of the LMMSE-based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance. Experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts
2226313
Fourier harmonic approach for visualizing temporal patterns of gene expression data
DNA microarray technology provides a broad snapshot of the state of the cell by measuring the expression levels of thousands of genes simultaneously. Visualization techniques can enable the exploration and detection of patterns and relationships in a complex dataset by presenting the data in a graphical format in which the key characteristics become more apparent. The purpose of this study is to present an interactive visualization technique conveying the temporal patterns of gene expression data in a form intuitive for nonspecialized end-users. The first Fourier harmonic projection (FFHP) was introduced to translate the multidimensional time series data into a two dimensional scatter plot. The spatial relationship of the points reflect the structure of the original dataset and relationships among clusters become two dimensional. The proposed method was tested using two published, array-derived gene expression datasets. Our results demonstrate the effectiveness of the approach.
5757371
A Semantic Framework for Distributed Applications
46136838
IPv6 traffic with multi-class QoS in VPN
Abstract This paper focuses on the modeling and performance analysis for IPv6 traffic with multi-class QoS in virtual private networks (VPNs). The multi-class QoS is implemented on differentiated service basis using priority scheme of 4 bits defined in the packet header of IPv6. A VPN-enabled IP router is modeled as a tandem queuing system in which each output link consists of two parallel priority output queues. The high-priority queue is used to carry the delay sensitive traffic while the low-priority queue is used to carry the delay insensitive traffic. On the other hand, multiple thresholds are implemented in each queue, respectively, for packet loss priority control. The performance analysis is done using fluid flow techniques. The numerical results obtained from the analysis show that the differentiated service based on the priority schemes defined in IPv6 is able to effectively satisfy the multi-class QoS requirement for supporting multimedia services in VPN. The performance trade-off between the delay sensitive traffic and delay insensitive traffic in terms of traffic throughput, packet loss probability and end-to-end delay in VPN networks is presented.