This article provides an overview of the performance and the theoretical complexity of approximate and exact methods for various versions of the shortest path problem. The proposed study aims to improve the resolution of a more general covering problem within a column generation scheme in which the shortest path problem is the sub-problem.

In this paper we consider the following covering problem. Given a set S of n points in d-dimensional space, d 2, nd two axis-parallel boxes that together cover the set S such that the measure of the largest box is minimized, where the measure is a monotone function of the box. We present a simple algorithm for nding boxes in O(n log n + n d?1) time and O(n) space.

We study in this paper a cutting-covering problem, defined by us in [2] and [3], the problem of covering a rectangular support with rectangular pieces cut from a roll. We first prove that the algorithm used in [2] and [3] for the rectangular cutting-covering problem without losses is not optimal. Starting from a decomposition of a natural number in sums of naturals we develop an algorithm for a...

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 study an NP-complete geometric covering problem called d-Dimensional Rectangle Stabbing, where, given a set of axis-parallel d-dimensional hyperrectangles, a set of axis-parallel (d − 1)-dimensional hyperplanes and a positive integer k, the question is whether one can select at most k of the hyperplanes such that every hyperrectangle is intersected by at least one of these hyperplanes. This ...

Given a clustered graph (G,V), that is, a graph G = (V,E) together with a partition V of its vertex set, the selective coloring problem consists in choosing one vertex per cluster such that the chromatic number of the subgraph induced by the chosen vertices is minimum. This problem can be formulated as a covering problem with a 0-1 matrix M(G,V). Nevertheless, we observe that, given (G,V), it i...

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...

In this paper we present current achievements in computer aided ECG analysis and their applicability in real world medical diagnosis process. Most of the current work is covering problems of removing noise, detecting heartbeats and rhythm-based analysis. There are some advancements in particular ECG segments detection and beat classifications but with limited evaluations and without clinical ap...

Depth-bounded processes form the most expressive known fragment of the π-calculus for which interesting verification problems are still decidable. In this paper we develop an adequate domain of limits for the well-structured transition systems that are induced by depth-bounded processes. An immediate consequence of our result is that there exists a forward algorithm that decides the covering pr...