2623430
Manifold reconstruction from point samples
We present an algorithm to "reconstruct" a smooth <i>k</i>-dimensional manifold <i>M</i> embedded in an Euclidean space R<sup>d</sup> from a "sufficiently dense" point sample from the manifold. The algorithm outputs a simplicial manifold that is homeomorphic and geometrically close to <i>M.</i> The running time is <i>O</i>(<i>n</i> log <i>n</i>) where <i>n</i> is the number of points in the sample (the multiplicative constant depends exponentially on the dimension though).
2549315
Quality meshing with weighted Delaunay refinement
Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic point sets, but not with boundaries. Recently a randomized point-placement strategy has been proposed to remove silvers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including silvers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay refinement paradigm.
359856
Curve reconstruction from noisy samples
We present an algorithm to reconstruct a collection of disjoint smooth closed curves from n noisy samples. Our noise model assumes that the samples are obtained by first drawing points on the curves according to a locally uniform distribution followed by a uniform perturbation of each point in the normal direction with a magnitude smaller than the minimum local feature size. The reconstruction is faithful with a probability that approaches 1 as n increases.We expect that our approach can lead to provable algorithms under less restrictive noise models and for handling non-smooth features.
7789266
LMT-skeleton heuristics for several new classes of optimal triangulations
Abstract Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle, and (3) the area balanced triangulation which minimizes the variance of the areas of triangles in the triangulation. With appropriate definition of local optimality for each class, a simple unified method is established for the computation of the subgraphs of optimal triangulations. Computational experiments demonstrate that the method successfully identifies large portion of edges of the optimal triangulations of each class for all problem instances tested, and hence optimal triangulations for each class can be obtained from them by applying dynamic programming.
5215240
Sliver exudation
A sliver is a tetrahedron whose four vertices lie close to a plane and whose projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3-dimensional Delaunay triangulations even for well-spaced point sets. We show that if the Delaunay triangulation has the ratio property introduced in [15] then there is an assignment of weights so the weighted Delaunay triangulation contains no slivers. We also give an algorithm to compute such a weight assignment.
17584518
On beta-skeleton as a subgraph of the minimum weight triangulation
Abstract Given a set S of n points in the plane, a triangulation is a maximal set of non-intersecting edges connecting the points in S . The weight of the triangulation is the sum of the lengths of the edges. In this paper, we show that for β>1/ sin κ , the β -skeleton of S is a subgraph of a minimum weight triangulation of S , where κ= tan −1 (3/ 2 3 )≈ π /3.1 . There exists a four-point example such that the β -skeleton for β sin ( π /3) is not a subgraph of the minimum weight triangulation.
20227157
Trellis coded color quantization of images
We examine color quantization of images using trellis coded quantization (TCQ). Together with a simple dithering scheme, an 8-bit trellis coded color quantizer reproduces images that are visually indistinguishable from the 24-bit originals. The proposed algorithm can be viewed as a predictive trellis coded color quantization scheme. It is universal in the sense that no training or lookup table is needed. The complexity of TCQ is linear with respect to image size, making trellis coded color quantization suitable for interactive graphics and a window-based display environment.
117206
On Integrated Location and Service Management for Minimizing Network Cost in Personal Communication Systems
We investigate the notion of per-user integrated location and service management in personal communication service (PCS) networks by which a Per-user service proxy is created to serve as a gateway between the mobile user and all client-server applications engaged by the mobile user. The service proxy is always colocated with the mobile user's location database such that whenever the MU's location database moves during a location handoff, a service handoff also ensues to colocate the service proxy with the location database. This allows the proxy to know the location of the mobile user all the time to reduce the network communication cost for service delivery. We investigate four integrated location and service management schemes. Our results show that the centralized scheme performs the best when the mobile user's SMR (service to mobility ratio) is low and CMR (call to mobility ratio) is high, while the fully distributed scheme performs the best when both SMR and CMR are high. In all other conditions, the dynamic anchor scheme is the best except when the service context transfer cost is high, under which the static anchor scheme performs the best. Through analytical and simulation results, we demonstrate that different users with vastly different mobility and service patterns should adopt different integrated location and service management methods to optimize system performance. Further, the best integrated scheme always performs better than the best decoupled scheme that considers location and service managements separately and management schemes that do not use any service proxy
1223930
Approximate Strategic Reasoning through Hierarchical Reduction of Large Symmetric Games
To deal with exponential growth in the size of a game with the number of agents, we propose an approximation based on a hierarchy of reduced games. The reduced game achieves savings by restricting the number of agents playing any strategy to fixed multiples. We validate the idea through experiments on randomly generated local-effect games. An extended application to strategic reasoning about a complex trading scenario motivates the approach, and demonstrates methods for game-theoretic reasoning over incompletely-specified games at multiple levels of granularity. Motivation Consider the task of selecting among a large set of strategies to play in an 8-player game. Through careful judgment you manage to narrow down the candidates to a reasonable number of strategies (say 35). Because the performance of a strategy for one agent depends on the strategies of the other seven, you wish to undertake a game-theoretic analysis of the situation. Determining the payoff for a particular strategy profile is expensive, however, as your observations of prior game instances are quite limited, and the only operational description of the game is in the form of a simulator that takes a non-negligible time (say 10 minutes) to produce one outcome. Moreover, since the environment is stochastic, numerous samples (say 12) are required to produce a reliable estimate for even one profile. At two hours per profile, ex
18292356
On dualities in multiterminal coding problems
It has been shown recently that under certain conditions there exist dualities between different multiterminal (MT) source and channel coding problems. Following these results, we study lossless MT source coding and deterministic MT channel coding problems and point out different dualities between them. In particular, we show that there exists a functional duality between a Slepian-Wolf (SW) coding problem and a deterministic broadcast channel (DBC) coding problem and between a lossless multiple-description (MD) coding problem and a deterministic multiple-access channel (DMAC) coding problem. In analogy to the duality established between DBC and DMAC coding problems, we further propose a similar duality between SW and lossless MD coding problems; in this way, we form a closed "duality loop" of four MT coding problems, which imposes the existence of a single common rate point in the achievable rate regions of all four dual problems. We also consider duality in zero-error MT coding and shed light on practical code design with an example. Finally, extension to the case with only one lossless/deterministic component in the source/channel coding problem is provided.
6666618
Low-Power Design for Real-Time Systems
Real-time Systems often are located in the special environments where the power consumption is a big concern. Upon presence of timing constraints, the low power design on the real-time systems has significant impact on the performance as well as the schedulability of the systems. The system developers are facing the challenges for reducing the power consumption and meeting the timing constraints in the real-time systems.This paper represents one of few attempts to address the issue of the low power design on real-time systems. We present two power reduction methods: one is at the software compilation level and the other at the operating system level. Given a real-time program, an inter-instruction power reduction technique is proposed to transform the program to another one with lower power consumption. In addition, a scheduling algorithm for real-time operating systems is proposed to reschedule real-time programs when the execution time of the programs is changed. Therefore, the proposed scheduling algorithm works together with the proposed power reduction technique to make sure all programs meet their deadlines and to improve the system schedulability. We also evaluate the performance of the proposed inter-instruction reduction method by comparing it with the cold scheduling algorithm and show that the proposed method outperforms the cold scheduling algorithm and reduces more energy power.