We present an improved inductive learning method to derive classification rules that correctly describe most of the examples belonging to a class and do not describe most of the examples not belonging to this class. The problem is represented as a modification of the set covering problems solved by a genetic algorithm. Its is employed to medical data on coronary disease, and the results seem to...

This paper presents a software platform for the distributed solution of complex optimization problems. For such problems there are often no outstanding approaches which always perform well. That is why we propose to use diierent solution methods simultaneously. They can communicate and thus prootate from each other. Some general paradigms are applicable to a wide class of problems. Our platform...

The Leech lattice is the exceptional lattice in dimension 24. Soon after its discovery by Leech [9], it was conjectured that it is extremal for several geometric problems in R: the kissing number problem, the sphere packing problem, and the sphere covering problem. In 1979, Odlyzko and Sloane and independently Levenshtein solved the kissing number problem in dimension 24 by showing that the Lee...

Thurston’s circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin-Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a circle packing metric in the disk with boundary circles internally tangent to the circle. The main proofs of the uniformization use hyperbolic volumes (Andr...

We present an inductive learning algorithm that allows for a partial completeness and consistence, i.e. that derives classification rules correctly describing, e.g, most of the examples belonging to a class and not describing most of the examples not belonging to this class. The problem is represented as a modification of the set covering problem that is solved by a greedy algorithm. The approa...

We describe the use of a tabu search algorithm for generating near minimum dominating sets in graphs. We demonstrate the eeectiveness of this algorithm by considering a previously studied class of graphs, the so-called \football pool" graphs, and improving many of the known upper bounds for this class.

1.1. We denote by V a connected ^-dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c = c(V) and c~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (| c1, | c~ |). We say that F i s ε-flat, ε > 0, if cd < ε. 1.2. Examples. a. Every compact flat manifold is ε-flat for any ε > 0. b. Every compact nil-manifold p...

A set of points and a positive integer m are given and our goal is to cover the maximum number of these point with m disks. We devise the first output sensitive algorithm for this problem. We introduce a parameter ρ as the maximum number of points that one disk can cover. In this paper first we solve the problem for m = 2 in O(nρ + ρ log ρ)) time. The previous algorithm for this problem runs in...

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on the vertex set, which are cost, capacity, and demand. The objective of this problem is to compute a demand assignment of least cost, such that the demand of e...