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...

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...

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...

Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusionexclusion ...

A family of discrete cooperative covering problems is analysed in this paper. Each facility emits a signal that decays by the distance and each demand point observes the total signal emitted by all facilities. A demand point is covered if its cumulative signal exceeds a given threshold. We wish to maximize coverage by selecting locations for p facilities from a given set of potential sites. Two...

We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U . A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set ...