On a Two-Dimensional Search Problem

In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.

Recognition on Finite Set of Events: Bayesian Analysis of Generalization Ability and Classification Tree Pruning

The problem of recognition on finite set of events is considered. The generalization ability of classifiers for this problem is studied within the Bayesian approach. The method for non-uniform prior distribution specification on recognition tasks is suggested. It takes into account the assumed degree of intersection between classes. The results of the analysis are applied for pruning of classification trees.

A Variable Neighborhood Search Approach for Solving the Maximum Set Splitting Problem

This paper presents a Variable neighbourhood search (VNS) approach for solving the Maximum Set Splitting Problem (MSSP). The algorithm forms a system of neighborhoods based on changing the component for an increasing number of elements. An efficient local search procedure swaps the components of pairs of elements and yields a relatively short running time. Numerical experiments are performed on the instances known in the literature: minimum hitting set and Steiner triple systems. Computational results show that the proposed VNS achieves all optimal or best known solutions in short times. The experiments indicate that the VNS compares favorably with other methods previously used for solving the MSSP. ACM Computing Classification System (1998): I.2.8.