Mining frequently appearing patterns in a database is a basic problem in informatics, especially in data mining. Particularly, when the input database is a collection of subsets of an itemset, the problem is called the frequent itemset mining problem, and has been extensively studied. In the real-world use, one of difficulties of frequent itemset mining is that real-world data is often incorrec...

Solovay [5] has proved that the minimal length of a program enumerating a set A is upper bounded by 3 times the negative logarithm of the probability that a random program will enumerate A. It is unknown whether one can replace the constant 3 by a smaller constant. In this paper, we show that the constant 3 can be replaced by the constant 2 for finite sets A. We recall first two complexity meas...

In this paper we examine the enumeration of alternating trees. We give a bijective proof of the fact that the number of alternating unrooted trees with n vertices is given by 1 n2 n?1 P n k=1 ? n k k n?1 , a problem rst posed by Postnikov in 4]. We also prove, using formal arguments, that the number of alternating plane trees with n vertices is 2(n ? 1) n?1 .

A positive definite quadratic form is called perfect, if it is uniquely determined by its arithmetical minimum and the integral vectors attaining it. In this self-contained survey we explain how to enumerate perfect forms in d variables up to arithmetical equivalence and scaling. We put an emphasis on practical issues concerning computer assisted enumerations. For the necessary theory of Vorono...

The search space for the feature selection problem in decision tree learning is the lattice of subsets of the available features. We provide an exact enumeration procedure of the subsets that lead to all and only the distinct decision trees. The procedure can be adopted to prune the search space of complete and heuristics search methods in wrapper models for feature selection. Based on this, we...