Computational complexity of queries based on itemsets

We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that despite the limitations our problems are also intractable, namely, we show that checking whether the maximal consistent frequency of a query is larger than a given threshold is NP-complete and that evaluating the Maximum Entropy estimate of a query is PP-hard. We also prove that checking consistency is NP-complete.     

Width-restricted layering of acyclic digraphs with consideration of dummy nodes

This paper deals with the problem of finding graph layerings restricted to a given maximal width. However, other than previous approaches for width-restricted layering, we take into account the space for dummy nodes, which are introduced by edges crossing a layer. The main result is that the problem of finding a width-restricted layering under consideration of dummy nodes is NP-complete even when all regular nodes have the same constant width and all dummy nodes have the same constant width.     

PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance

We consider the problem of PAC-learning distributions over strings, represented by probabilistic deterministic finite automata (PDFAs). PDFAs are a probabilistic model for the generation of strings of symbols, that have been used in the context of speech and handwriting recognition, and bioinformatics. Recent work on learning PDFAs from random examples has used the KL-divergence as the error measure; here we use the variation distance. We build on recent work by Clark and Thollard, and show that the use of the variation distance allows simplifications to be made to the algorithms, and also a strengthening of the results; in particular that using the variation distance, we obtain polynomial sample size bounds that are independent of the expected length of strings.     

The complexity of some reachability problems for a system on a finite group

We consider a system defined as the product of a finite set of periodic systems on cyclic groups. It is of interest to determine if certain subgroups and unions of subgroups of the state set are reachable from a specified initial state, and in particular to determine the computational complexity of verifying such reachability. These questions are motivated by certain problems that arise in the modelling and control of discrete event systems and certain forms of periodic scheduling. Our main result is that deciding whether or not the union of a certain set of subgroups is reachable or not is NP-complete.     

The vulnerability of geometric sequences based on fields of odd characteristic

A new method of cryptologic attack on binary sequences is given, using their linear complexities relative to odd prime numbers. We show that, relative to a particular prime number p, the linear complexity of a binary geometric sequence is low. It is also shown that the prime p can be determined with high probability by a randomized algorithm if a number of bits much smaller than the linear complexity is known. This determination is made by exploiting the imbalance in the number of zeros and ones in the sequences in question, and uses a new statistical measure, the partial imbalance.This project was sponsored by the National Security Agency under Grant No. MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.     

Disentangling the Sources of Opioid Withdrawal Responses: Comment on McDonald and Siegel (2004).

R. V. McDonald and S. Siegel (see record 2004-10475-001) present new evidence for the idea that opioid drug-opposite responses can become conditioned to cues of initial drug onset and that they could, therefore, play a role in the development of tolerance of some drug effects and a role in the elicitation of withdrawal-like symptoms in cases in which addicted individuals are exposed to small doses of the drug they normally consume. In this comment, some puzzling features of the data are discussed, and alternative explanations are suggested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

求解机械装配规划的新方法

本文提出一个求解机械装配规划的算法,其计算量～O(sN~2),其中s是零件所有可能装配方向的个数,N是工件的零件数(一般s～O(N)).而现行的求机械装配规划的算法,其计算量均随N的增加按指数律增加.     

Minimizing the number of tool switches on a flexible machine

This article analyzes a tool switching problem arising in certain flexible manufacturing environments. A batch of jobs have to be successively processed on a single flexible machine. Each job requires a subset of tools, which have to be placed in the tool magazine of the machine before the job can be processed. The tool magazine has a limited capacity, and, in general, the number of tools needed to produce all the jobs exceeds this capacity. Hence, it is sometimes necessary to change tools between two jobs in a sequence. The problem is then to determine a job sequence and an associated sequence of loadings for the tool magazine, such that the total number of tool switches is minimized. This problem has been previously considered by several authors; it is here revisited, both from a theoretical and from a computational viewpoint. Basic results concerning the computational complexity of the problem are established. Several heuristics are proposed for its solution, and their performance is computationally assessed.     

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’).     

Smaller superconcentrators of density 28

An N-superconcentrator is a directed, acyclic graph with N input nodes and N output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. Here it is proved that such superconcentrators exist (by a random construction of certain expander graphs as building blocks) having density 28 (where the density is the number of edges divided by N). The best known density before this paper was 34.2 [U. Schöning, Construction of expanders and superconcentrators using Kolmogorov complexity, J. Random Structures Algorithms 17 (2000) 64-77] or 33 [L.A. Bassalygo, Personal communication, 2004].