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ÐThe paper describes a new, logic-based methodology for analyzing observations. The key features of the Logical Analysis of Data (LAD) are the discovery of minimal sets of features necessary for explaining all observations and the detection of hidden patterns in the data capable of distinguishing observations describing ªpositiveº outcome events from(More)
In this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary " true n-vectors " (or " positive examples ") and a set of " false n-vectors " (or " negative examples "), we establish a Boolean function (or an extension) f , so that f is true (resp., false) in every given true(More)
We provide constant ratio approximation algorithms for two NP-hard problems, the rectangle stabbing problem and the rectilinear partitioning problem. In the rectangle stabbing problem, we are given a set of rectangles in two-dimensional space, with the objective of stabbing all rectangles with the minimum number of lines parallel to the x and y axes. We(More)
The set covering problem (SCP) asks to choose a minimum cost family of subsets from given n subsets, which together covers the entire ground set. In this paper, we propose a local search algorithm for SCP, which have the following three features. (1) The use of 3-BLOCKINip neighborhood, which is the set of solutions obtainable from the current solution by(More)