5430944
Distributed selfish load balancing
Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a "selfish agent", and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced.Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ε-Nash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n4). We also give a lower bound of Ω (max{log log m, n}) for the convergence time.
18074193
Dynamic Diffusion Load Balancing
We consider the problem of dynamic load balancing in arbitrary (connected) networks on n nodes. Our load generation model is such that during each round, n tasks are generated on arbitrary nodes, and then (possibly after some balancing) one task is deleted from every non-empty node. Notice that this model fully saturates the resources of the network in the sense that we generate just as many new tasks per round as the network is able to delete. We show that even in this situation the system is stable, in that the total load remains bounded (as a function of n alone) over time. Our proof only requires that the underlying “communication” graph be connected. (It of course also works if we generate less than n new tasks per round, but the major contribution of this paper is the fully saturated case.) We further show that the upper bound we obtain is asymptotically tight (up to a moderate multiplicative constant) by demonstrating a corresponding lower bound on the system load for the particular example of a linear array (or path). We also show some simple negative results (i.e., instability) for work-stealing based diffusion-type algorithms in this setting.
94046
Rapidly mixing Markov chains for sampling contingency tables with a constant number of rows
We consider the problem of sampling almost uniformly from the set of contingency tables with given row and column sums, when the number of rows is a constant. (2002) have recently given a fully polynomial randomized approximation scheme (fpras) for the related counting problem, which only employs Markov chain methods indirectly. But they leave open the question as to whether a natural Markov chain on such tables mixes rapidly. Here we answer this question in the affirmative, and hence provide a very different proof of the main result of Cryan and Dyer. We show that the "2 /spl times/ 2 heat-bath" Markov chain is rapidly mixing. We prove this by considering first a heat-bath chain operating on a larger window. Using techniques developed by Morris and Sinclair (2002) (see also Morris (2002)) for the multidimensional knapsack problem, we show that this chain mixes rapidly. We then apply the comparison method of Diaconis and Saloff-Coste (1993) to show that the 2 /spl times/ 2 chain is rapidly mixing. As part of our analysis, we give the first proof that the 2 /spl times/ 2 chain mixes in time polynomial in the input size when both the number of rows and the number of columns is constant.
12022403
Numerical methods for beautification of reverse engineered geometric models
Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and the model building software. The quality of such models can be improved in a beautification step, which finds geometric regularities approximately present in the model and tries to impose a consistent subset of these regularities on the model. A framework for beautification and numerical methods to select and solve a consistent set of constraints deduced from a set of regularities are presented. For the initial selection of consistent regularities likely to be part of the model's ideal design priorities, and rules indicating simple inconsistencies between the regularities are employed. By adding regularities consecutively to an equation system and trying to solve it by using quasi-Newton optimization methods, inconsistencies and redundancies are detected. The results of experiments are encouraging and show potential for an expansion of the methods based on degree of freedom analysis.
2549795
Disassembly sequences for objects built from unit cubes
The geometrical problem of finding a possible disassembly sequence for an object is considered for a limited class of objects: those whose parts can be made from collections of unit cubes. For such objects, we consider motions of their component parts which are translations in one of three orthogonal directions. 
 
A working program has been implemented in pop-11, which finds a disassembly sequence for an object defined by a 3D cube map. Each disassembly step may consist of either one or two linear motions of single parts. Removal of subassemblies consisting of more than one part is not considered. 
 
To ensure properly the validity of a disassembly motion, both local and global geometric information must be considered. The local geometric feasibility of a motion relates to whether an infinitesimal motion can be made, and it is determined by the surface contacts (mates) between a part and other parts. The global geometric feasibility of a motion relates to whether a finite (or infinite) motion can be made in a particular direction. It depends not only on the relationship between the part to be moved and those that it touches, but also on its relationship with, potentially, all the other parts in the assembly. To determine the global geometric feasibility of a motion, the idea of coupling between two faces is introduced. Coupling is a directional quantity which gives the finite limit on the relative motion between two faces. By considering the coupling information for all the faces of a part, it is easy to determine the finite motions that are possible in any direction.
37569271
Building Panoramas from Photographs Taken with an Uncalibrated Hand-Held Camera
1245254
Approximate symmetry detection for reverse engineering
The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. B-rep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable B-rep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n 3.5 log4 n), and a justification is given that on common engineering objects it takes about O(n2 log4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.
12804235
Finding Approximate Shape Regularities for Reverse Engineering
Current reverse engineering systems can generate boundary representation (B-rep) models from 3D range data. Such models suffer from inaccuracies caused by noise in the input data and algorithms. The quality of reverse engineered geometric models can be improved by finding candidate shape regularities in such a model, and constraining the model to meet a suitable subset of them, in a post-processing step called beautification. This paper discusses algorithms to detect such approximate regularities in terms of similarities between feature objects describing properties of faces, edges and vertices, and small groups of these elements in a B-rep model with only planar, spherical, cylindrical, conical and toroidal faces. For each group of similar feature objects they also seek special feature objects which may represent the group, e.g. an integer value which approximates the radius of similar cylinders. Experiments show that the regularities found by the algorithms include the desired regularities as well as spurious regularities, which can be limited by an appropriate choice of tolerances.