The calculation of an exact minimal cover of a Boolean function is an NP -complete problem. In this paper we introduce the definition of this problem and its basic solution. By using a slightly modified algorithm, we get a speed-up factor of more than 10. The main contributions of this paper are the description of an alternative approach mentioned in [15], and a remarkable improvement of this a...

Using satellite radar interferometry observations of Greenland, we detected widespread glacier acceleration below 66 degrees north between 1996 and 2000, which rapidly expanded to 70 degrees north in 2005. Accelerated ice discharge in the west and particularly in the east doubled the ice sheet mass deficit in the last decade from 90 to 220 cubic kilometers per year. As more glaciers accelerate ...

We take a new look at the multicut problem in trees through the eyes of the vertex cover problem. This connection, together with other techniques that we develop, allows us to significantly improve the O(k) upper bound on the kernel size for multicut, given by Bousquet et al., to O(k). We exploit this connection further to present a parameterized algorithm for multicut that runs in time O∗(ρk),...

A set P of edge-disjoint paths in a graph G is called an edge-covering of G if every edge of G is contained in a path of P. The path edge-covering number of G is then defined as the smallest number p(G) of paths in such an edge-covering of G. This parameter appeared in the study of certain models of information retrieval structures (see, e. g., [6]). If we are considering a tree T , then it is ...

We consider a natural generalization of the classical minimum hitting set problem, the minimum hitting set of bundles problem (mhsb) which is defined as follows. We are given a set E = {e1, e2, . . . , en} of n elements. Each element ei (i = 1, . . . , n) has a non negative cost ci. A bundle b is a subset of E . We are also given a collection S = {S1, S2, . . . , Sm} of m sets of bundles. More ...

The Set Cover problem belongs to a group of hard problems which are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. In recent years, many researchers design exact exponential-time algorithms for problems of that kind. The goal is getting the time complexity still of order O(c), but with the co...

Several approximation algorithms with proven performance guarantees have been proposed to find approximate solutions to classical combinatorial optimization problems. However, theoretical results may not reflect the experimental performance of the proposed algorithms. As a consequence, a question arises: how “far” from the theoretically proved performance are the experimental results?We conduct...

Eigenvectors of the Laplacian of a cycle graph exhibit the sinusoidal characteristics of the standard DFT basis, and signals defined on such graphs are amenable to linear shift invariant (LSI) operations. In this paper we propose to reduce a generic graph to its vertex-disjoint cycle cover, i.e., a set of subgraphs that are cycles, that together contain all vertices of the graph, and no two sub...

Databases containing varied linguistic features can be build by condensing large corpora; in this work we need to cover a set of phonetic units with a minimal set of natural phonetic sentences. With this aim in view we compare three set covering methods: the greedy method, its inverse which we call the spitting method, and the pair exchange method. Each method is defined with several criteria g...