On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving

In this paper we analyze the algebraic formulations of certain geometry statements appearing in recent literature related to mechanical geometry theorem proving and give several examples to show that one of these formulations can cause serious problems. We clarify a formulation which is essentially due to W. T. Wu and, in our opinion, is the most satisfactory.This author was supported by NSF Grants DCR-8503498 and CCR-8702108.     

A genetic algorithm for the optimisation of assembly sequences

This paper describes a Genetic Algorithm (GA) designed to optimise the Assembly Sequence Planning Problem (ASPP), an extremely diverse, large scale and highly constrained combinatorial problem. The modelling of the ASPP problem, which has to be able to encode any industrial-size product with realistic constraints, and the GA have been designed to accommodate any type of assembly plan and component. A number of specific modelling issues necessary for understanding the manner in which the algorithm works and how it relates to real-life problems, are succinctly presented, as they have to be taken into account/adapted/solved prior to Solving and Optimising (S/O) the problem. The GA has a classical structure but modified genetic operators, to avoid the combinatorial explosion. It works only with feasible assembly sequences and has the ability to search the entire solution space of full-scale, unabridged problems of industrial size. A case study illustrates the application of the proposed GA for a 25-components product.     

Neural Networks Analysis of Steel Plate Processing Augmented by Multi‐objective Genetic Algorithms

An earlier neural network analysis of processing of steel plates through hot rolling was subjected to a further refined analysis through some flexible neural networks that evolved using a multi‐objective predator‐prey genetic algorithm. The original data set expressing the Yield Strength and Ultimate Tensile Strength of the rolled slabs in terms of a total of 108 process variables were subjected to a systematic pruning through this evolutionary approach, till the nitrogen content of the steel emerged as the most significant input variable. A theoretical explanation is provided for this slightly unexpected result.     

Nonnegative integral subset representations of integer sets

We consider an integer-subset representation problem motivated by a medical application in radiation therapy. We prove NP-completeness, derive nontrivial bounds, and report on the performance of a greedy heuristic.     

Accelerating Refractive Rendering of Transparent Objects

In this paper, a technique is proposed for the rendering of transparent objects interactively using the method of refractive rendering. In the proposed technique, the refractive rendering algorithm is performed in two stages, namely the pre‐computation stage and the shading stage. In the pre‐computation stage, ray‐traced information, including directions and positions of rays, are generated by a ray tracing process and are stored in a set of ray lists. In the shading stage, these data are retrieved from the ray lists for computing the shading of an object. Using the proposed technique, photorealistic image of transparent objects and gemstones with various cuttings, material properties, lighting and background can be rendered interactively. By combining the refractive rendering technique with conventional shading techniques, jewelry and crystal designs can be rendered at a much higher speed comparing with conventional ray tracing techniques.     

Canonical density control

The Sparse Table is a data structure for controlling density in an array which was first proposed in 1981 and has recently reappeared as a component of cache-oblivious data structures. All existing variants of the Sparse Table divide the array into blocks that have a calibrator tree above them. We show that the same amortized complexity can be achieved without this auxiliary structure, obtaining a canonical data structure that can be updated by conceptually simpler algorithms.     

Linear self-stabilizing algorithms for the independent and dominating set problems using an unfair distributed scheduler

This paper presents distributed self-stabilizing algorithms for the maximal independent and the minimal dominating set problems. Using an unfair distributed scheduler the algorithms stabilizes in at most max{3n−5,2n} resp. 9n moves. All previously known algorithms required O(n²) moves.     

Accurate Depth of Field Simulation in Real Time

We present a new post processing method of simulating depth of field based on accurate calculations of circles of confusion. Compared to previous work, our method derives actual scene depth information directly from the existing depth buffer, requires no specialized rendering passes, and allows easy integration into existing rendering applications. Our implementation uses an adaptive, two‐pass filter, producing a high quality depth of field effect that can be executed entirely on the GPU, taking advantage of the parallelism of modern graphics cards and permitting real time performance when applied to large numbers of pixels.     

Metaheuristic downhill simplex method in combinatorial optimization

The concept of combinatorial objects is formalized. It allows strict definition of a combinatorial optimization problem (COP). An efficient metaheuristic method to solve COPs (H-method) is considered. It includes stochastic local search algorithms as a built-in procedure. A parallel implementation of the H-method is set forth and analyzed. The results from a numerical experiment and solution of some well-known COPs on personal computers and on the SKIT cluster supercomputer are presented. The study was supported by INTAS (Project 06-1000017-8909). __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 70–79, November–December 2007.     

Optimal implementations of UPGMA and other common clustering algorithms

In this work we consider hierarchical clustering algorithms, such as UPGMA, which follow the closest-pair joining scheme. We survey optimal O(n²)-time implementations of such algorithms which use a ‘locally closest’ joining scheme, and specify conditions under which this relaxed joining scheme is equivalent to the original one (i.e. ‘globally closest’).