On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.This work was partially supported by the National Science Foundation's US-Italy Collaborative Research Program under Grant INT-8714578 and Information, Robotics, and Intelligent Research Grant IRI-8704781.     

排序聚类分析算法在派生式CAPP系统中的应用及实现

利用零件的相似性原理对零件分组是派生式CAPP系统的重要内容,对零件的分组是否合理,直接影响到派生式CAPP系统能否正常运行。阐述了排序聚类分析算法在生产流程分析法中的工作原理,分析了利用该算法实现零件分组的实现过程,并用示例验证了该算法。     

Networks for sorting multitonic sequences

Lee and Batcher have designed networks that efficiently merge k separately provided sorted sequences of known lengths totalling n. We show that the design is still possible, and in fact easier to describe, if we do not make use of the lengths, or even the directions of monotonicity, of the individual sequences—the sequences can be provided in a single undelimited concatenation of length n. The depth of the simplest resulting network to sort sequences that are “k-tonic” and of length n is , generalizing Batcher's 1968 results for the extreme values of k (k=2 corresponding to merging, and k=n/2 corresponding to general sorting).The exposition is self-contained and can serve even as an introduction to sorting networks and Batcher's results.     

MULTICRITERIA SORTING METHODOLOGY: APPLICATION TO FINANCIAL DECISION PROBLEMS

Abstract

The primary objective in the sorting approach is to assign a set of alternatives into predefined classes. This type of problem is often encountered in many real world decision problems. During the last two decades several new approaches have been proposed to overcome the shortcomings of traditional statistical and econometric techniques. This paper focuses on the multicriteria decision aid (MCDA) approach; it briefly reviews the main MCDA sorting techniques, and presents the multigroup hierarchical discrimination method. This new MCDA sorting technique is applied to the portfolio selection problem. A comparison with discriminant analysis is also performed. Furthermore, the efficiency of the proposal approach can be easily improved for solving large-scale problems in a multiprocessing environment.     

Sorting streamed multisets

Sorting is a classic problem and one to which many others reduce easily. In the streaming model, however, we are allowed only one pass over the input and sublinear memory, so in general we cannot sort. In this paper we show that, to determine the sorted order of a multiset s of size n containing σ?2 distinct elements using one pass and o(nlogσ) bits of memory, it is generally necessary and sufficient that its entropy H=o(logσ). Specifically, if s={s₁,…,sn} and si₁,…,sin is the stable sort of s, then we can compute i₁,…,in in one pass using O((H+1)n) time and O(Hn) bits of memory, with a simple combination of classic techniques. On the other hand, in the worst case it takes that much memory to compute any sorted ordering of s in one pass.     

Maximum likelihood analysis of algorithms and data structures

We present a new approach for an average-case analysis of algorithms and data structures that supports a non-uniform distribution of the inputs and is based on the maximum likelihood training of stochastic grammars. The approach is exemplified by an analysis of the expected size of binary tries as well as by three sorting algorithms and it is compared to the known results that were obtained by traditional techniques. Investigating traditional settings like the random permutation model, we rediscover well-known results formerly derived by pure analytic methods; changing to biased data yields original results. All but one step of our analysis can be automated on top of a computer-algebra system. Thus our new approach can reduce the effort required for an average-case analysis, allowing for the consideration of realistic input distributions with unknown distribution functions at the same time. As a by-product, our approach yields an easy way to generate random combinatorial objects according to various probability distributions.     

Simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection

Tolerance specification is an important part of mechanical design. Design tolerances strongly influence the functional performance and manufacturing cost of a mechanical product. Tighter tolerances normally produce superior components, better performing mechanical systems and good assemblability with assured exchangeability at the assembly line. However, unnecessarily tight tolerances lead to excessive manufacturing costs for a given application. The balancing of performance and manufacturing cost through identification of optimal design tolerances is a major concern in modern design. Traditionally, design tolerances are specified based on the designer’s experience. Computer-aided (or software-based) tolerance synthesis and alternative manufacturing process selection programs allow a designer to verify the relations between all design tolerances to produce a consistent and feasible design. In this paper, a general new methodology using intelligent algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Particle Swarm Optimization (MOPSO) for simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection is presented. The problem has a multi-criterion character in which 3 objective functions, 3 constraints and 5 variables are considered. The average fitness factor method and normalized weighted objective functions method are separately used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.