Manufacturing complexity analysis

The analysis of the complexity of a typical system is presented. Starting with the subsystems of an example system, the step-by-step procedure for analysis of the complexity of an overall system is given. The learning curves for the various subsystems are determined as well as the concurrent numbers of relevant design parameters. Then trend curves are plotted for the learning curve slopes versus the various design-oriented parameters, e.g. number of parts versus slope of learning curve, or number of fasteners versus slope of learning curve, etc. Representative cuts are taken from each trend curve, and a figure-of-merit analysis is made for each of the subsystems. Based on these values, a characteristic curve is plotted which is indicative of the complexity of the particular subsystem. Each such characteristic curve is based on a universe of trend curve data taken from data points observed for the subsystem in question. Thus, a characteristic curve is developed for each of the subsystems in the overall system

Complexity analysis of the stock market

We study the complexity of the stock market by constructing $\epsilon$-machines of Standard and Poor's 500 index from February 1983 to April 2006 and by measuring the statistical complexities. It is found that both the statistical complexity and the number of causal states of constructed $\epsilon$-machines have decreased for last twenty years and that the average memory length needed to predict the future optimally has become shorter. These results support that the information is delivered to the economic agents and applied to the market prices more rapidly in year 2006 than in year 1983.Comment: 9 pages, 4 figure

Modular Complexity Analysis for Term Rewriting

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to their restricted power. To overcome this limitation the article introduces a modular framework which allows to infer (polynomial) upper bounds on the complexity of term rewrite systems by combining different criteria. Since the fundamental idea is based on relative rewriting, we study how matrix interpretations and match-bounds can be used and extended to measure complexity for relative rewriting, respectively. The modular framework is proved strictly more powerful than the conventional setting. Furthermore, the results have been implemented and experiments show significant gains in power.Comment: 33 pages; Special issue of RTA 201

A complexity analysis of statistical learning algorithms

We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order operations (e.g., certain optimizations) are considered primitive for the purposes of measuring complexity. We consider classes of information operators and algorithms made up of scaled families, and investigate the utility of scaling the complexities to minimize error. We look at the division of statistical learning into information and algorithmic components, at the complexities of each, and at applications to support vector machine (SVM) and more general machine learning algorithms. We give applications to SVM algorithms graded into linear and higher order components, and give an example in biomedical informatics

Time complexity analysis of generalized decomposition algorithm

The time complexity of the fast algorithm for generalized disjunctive decomposition of an rvalued function is studied.The considered algorithm to find the best decomposition is based on the analysis of multiple-terminal multiple-valued decision diagrams. It is shown that the time complexity for random rvalued functions depends on the such restriction as the number n1 of inputs in the first level circuit. In the case where the best partition of input variables is searched with restriction the time complexity is reduced in several times. The algorithm was simulated on a digital computer. The experimental results are in agreement with the theoretical predictions

Complexity Analysis of Balloon Drawing for Rooted Trees

In a balloon drawing of a tree, all the children under the same parent are placed on the circumference of the circle centered at their parent, and the radius of the circle centered at each node along any path from the root reflects the number of descendants associated with the node. Among various styles of tree drawings reported in the literature, the balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. For each internal node in a balloon drawing, the ray from the node to each of its children divides the wedge accommodating the subtree rooted at the child into two sub-wedges. Depending on whether the two sub-wedge angles are required to be identical or not, a balloon drawing can further be divided into two types: even sub-wedge and uneven sub-wedge types. In the most general case, for any internal node in the tree there are two dimensions of freedom that affect the quality of a balloon drawing: (1) altering the order in which the children of the node appear in the drawing, and (2) for the subtree rooted at each child of the node, flipping the two sub-wedges of the subtree. In this paper, we give a comprehensive complexity analysis for optimizing balloon drawings of rooted trees with respect to angular resolution, aspect ratio and standard deviation of angles under various drawing cases depending on whether the tree is of even or uneven sub-wedge type and whether (1) and (2) above are allowed. It turns out that some are NP-complete while others can be solved in polynomial time. We also derive approximation algorithms for those that are intractable in general