2559456
Parametric and kinetic minimum spanning trees
We consider the parametric minimum spanning tree problem, in which we are given a graph with edge weights that are linear functions of a parameter /spl lambda/ and wish to compute the sequence of minimum spanning trees generated as /spl lambda/ varies. We also consider the kinetic minimum spanning tree problem, in which /spl lambda/ represents time and the graph is subject in addition to changes such as edge insertions, deletions, and modifications of the weight functions as time progresses. We solve both problems in time O(n/sup 2/3/log/sup 4/3/) per combinatorial change in the tree (or randomized O(n/sup 2/3/log/sup 4/3/ n) per change). Our time bounds reduce to O(n/sup 1/2/log/sup 3/2/ n) per change (O(n/sup 1/2/log n) randomized) for planar graphs or other minor-closed families of graphs, and O(n/sup 1/4/log/sup 3/2/ n) per change (O(n/sup 1/4/ log n) randomized) for planar graphs with weight changes but no insertions or deletions.
2650108
Lightweight sensing and communication protocols for target enumeration and aggregation
The development of lightweight sensing andcommunication protocols is a key requirement for designing resource constrained sensor networks. This paper introduces a set of efficient protocols and algorithms, DAM, EBAM, and EMLAM, for constructing and maintaining sensor aggregates that collectively monitor target activity in the environment. A sensor aggregate comprises those nodes in a network that satisfy a grouping predicate for a collaborative processing task. The parameters of the predicate depend on the task and its resource requirements. Since the foremost purpose of a sensor network is to selectively gather information about the environment, the formation of appropriate sensor aggregates is crucial for optimally allocating resources to sensing and communication tasks.This paper makes minimal assumptions about node onboard processing and communication capabilities so as to allow possible implementations on resource-constrained hardware. Factors affecting protocol performance are discussed. The paper presents simulation results showing how the protocol performance varies as key network and task parameters are varied. It also provides probabilistic analyses of network behavior consistent with the simulation results. The protocols have been experimentally validated on a sensor network testbed comprising 25 Berkeley MICA sensor motes.
10626633
Cylindrical static and kinetic binary space partitions
We describe the first known algorithm for efficiently maintaining a Binary Space Partition (BSP) for n continuously moving segments in the plane, whose interiors remain disjoint throughout the motion. Under reasonable assumptions on the motion, we show that the total number of times this BSP changes is O.n 2 / ,a nd that we can update the BSP in O.logn/ expected time per change. Throughout the motion, the expected size of the BSP is O.n logn/. We also consider the problem of constructing a BSP for n static triangles with pairwise-disjoint interiors in R 3 . We present a randomized algorithm that constructs a BSP of size O.n 2 / in O.n 2 log 2 n/ expected time. We also describe a deterministic algorithm that constructs a BSP of size O..nCk/log 2 n/ and height O.logn/ in O..nCk/log 3 n/ time, where k is the number of intersection points between the edges of the projections of the triangles onto the xy-plane. This is the first known algorithm that constructs a BSP of O.logn/ height for disjoint triangles inR 3 . © 2000 Elsevier Science B.V. All rights reserved.
2060671
Landmark Selection and Greedy Landmark-Descent Routing for Sensor Networks
We study the problem of landmark selection for landmark-based routing in a network of fixed wireless communication nodes. We present a distributed landmark selection algorithm that does not rely on global clock synchronization, and a companion local greedy landmark-based routing scheme. We assume no node location information, and that each node can communicate with some of its geographic neighbors. Each node is named by its hop count distances to a small number of nearby landmarks. Greedy routing at a node is performed to equalize its vector of landmark distances to that of the destination. This is done by following the shortest path to the landmark that maximizes the ratio of its distances to the source and the destination. In addition, we propose a method to alleviate the difficulty in routing to destinations near the boundaries by virtually expanding the network boundaries. The greedy routing, when combined with our landmark selection scheme, has a provable bounded path stretch relative to the best path possible, and guarantees packet delivery in the continuous domain. In the discrete domain, our simulations show that the landmark selection scheme is effective, and the companion routing scheme performs well under realistic settings. Both the landmark selection and greedy routing assumes no specific communication model and works with asymmetric links. Although some of the analysis are non-trivial, the algorithms are simple, flexible and cost-effective enough to warrant a real-world deployment.
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.
36092896
Fractionally cascaded information in a sensor network
1832504
Metropolis light transport
We present a new Monte Carlo method for solving the light transport problem, inspired by the Metropolis sampling method in computational physics. To render an image, we generate a sequence of light transport paths by randomly mutating a single current path (e.g. adding a new vertex to the path). Each mutation is accepted or rejected with a carefully chosen probability, to ensure that paths are sampled according to the contribution they make to the ideal image. We then estimate this image by sampling many paths, and recording their locations on the image plane. Our algorithm is unbiased, handles general geometric and scattering models, uses little storage, and can be orders of magnitude more efficient than previous unbiased approaches. It performs especially well on problems that are usually considered difficult, e.g. those involving bright indirect light, small geometric holes, or glossy surfaces. Furthermore, it is competitive with previous unbiased algorithms even for relatively simple scenes. The key advantage of the Metropolis approach is that the path space is explored locally, by favoring mutations that make small changes to the current path. This has several consequences. First, the average cost per sample is small (typically only one or two rays). Second, once an important path is found, the nearby paths are explored as well, thus amortizing the expense of finding such paths over many samples. Third, the mutation set is easily extended. By constructing mutations that preserve certain properties of the path (e.g. which light source is used) while changing others, we can exploit various kinds of coherence in the scene. It is often possible to handle difficult lighting problems efficiently by designing a specialized mutation in this way. CR Categories: I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation; G.1.9 [Numerical Analysis]: Integral Equations—Fredholm equations.
7378273
Learning smooth objects by probing
This video considers the problem of discovering the boundary S of an unknown smooth object O. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We present a probing strategy for generating a sequence of sample points of S, from which a PL-approximation of S can be constructed, within any desired accuracy. This strategy can be applied in any dimension, although its output is guaranteed only for objects embedded in the plane or in 3-space. For pedagogical purpose, the video focuses on the planar case.
1985585
A Computational Framework for Handling Motion
We present a framework for implementing geometric algorithms involving motion. It is written in C++ and modeled after and makes extensive use of CGAL (Computational Geometry Algorithms Library) [4]. The framework allows easy implementation of kinetic data structure style geometric algorithms—ones in which the combinatorial structure changes only at discrete times corresponding to roots of functions of the motions of the primitives. This paper discusses the architecture of the framework and how to use it. We also briefly present a polynomial package we wrote, that supports exact and filtered comparisons of real roots of polynomials and is extensively used in the framework. We plan to include our framework in the next release of CGAL.
34799453
Estimating surface normals in noisy point cloud data
In this paper we describe and analyze a method based on local least square fitting for estimating the normals at all sample points of a point cloud data (PCD) set, in the presence of noise. We study the effects of neighborhood size, curvature, sampling density, and noise on the normal estimation when the PCD is sampled from a smooth curve in ℝ2 or a smooth surface in ℝ3, and noise is added. The analysis allows us to find the optimal neighborhood size using other local information from the PCD. Experimental results are also provided.
1377102
Meshless animation of fracturing solids
We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.