Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Модельное Описание Процессов Развития: Механизмы, Структура, Система Целей, Индикаторы

В постановочном плане рассмотрены вопросы введения понятия «пространство развития», виды возможных изменений системы, структура и механизмы развития. Рассмотрены типологии индикаторов развития, роль информационной компоненты и понятия качества.

On the Time Complexity of the Problem Related to Reducts of Consistent Decision Tables

In recent years, rough set approach computing issues concerning reducts of decision tables have attracted the attention of many researchers. In this paper, we present the time complexity of an algorithm computing reducts of decision tables by relational database approach. Let DS = (U, C ∪ {d}) be a consistent decision table, we say that A ⊆ C is a relative reduct of DS if A contains a reduct of DS. Let s = be a relation schema on the attribute set C ∪ {d}, we say that A ⊆ C is a relative minimal set of the attribute d if A contains a minimal set of d. Let Qd be the family of all relative reducts of DS, and Pd be the family of all relative minimal sets of the attribute d on s. We prove that the problem whether Qd ⊆ Pd is co-NP-complete. However, the problem whether Pd ⊆ Qd is in P .

Digraphs Definition for an Array Maintenance Problem

In this paper we present a data structure which improves the average complexity of the operations of updating and a certain type of retrieving information on an array. The data structure is devised from a particular family of digraphs verifying conditions so that they represent solutions for this problem.

An Effective Method for Constructing Data Structures Solving an Array Maintenance Problem

In this paper a constructive method of data structures solving an array maintenance problem is offered. These data structures are defined in terms of a family of digraphs which have previously been defined, representing solutions for this problem. We present as well a prototype of the method in Haskell.

Application of the Heterogeneous System Prediction Method to Pattern Recognition Problem

* This work was financially supported by RFBR-04-01-00858.

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.