Given a family of subsets S = {S1, . . . , Sm} over a set of elements X = {x1, . . . , xn} and an integer p, max k-set cover consists of finding a set T of at most k subsets covering at least p elements. This problem, when parameterized by k, can be easily shown to be W[2]-hard. Here, we settle the parameterized complexity of max k-set cover under several parameters as max{k,∆}, where ∆ = maxi{...

We study the complexity of several parameterizations for max k-set cover. Given a family of subsets S = {S1, . . . , Sm} over a set of elements X = {x1, . . . , xn} and an integer p, max k-set cover consists of finding a set T of at most k subsets covering at least p elements. This problem, when parameterized by k, is W[2]-hard. Here, we settle the multiparameterized complexity of max k-set cov...

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. The two rules that we characterize are the ma...

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relati...

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a Þnite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relatio...

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...

As with many min-max characterizations, proving one of the inequalities is straightforward. For any U ⊆ S and I ∈ I1 ∩ I2, we have |I| = |I ∩ U |+ |I ∩ (S \ U)| ≤ r1(U) + r2(S \ U), since I ∩ U is an independent set in I1 and I ∩ (S \ U) is an independent set in I2. Therefore, maxI∈I1∩I2 |I| ≤ minU∈S (r1(U) + r2(S \ U)). The following important examples illustrate some of the applications of th...

AIM Left ventricular rotation is an interesting mechanism to investigate patients with heart disease. In children, reference values have to be defined prior to assess pathology. METHODS AND RESULTS One hundred and seventy-four healthy individuals (0-20 years) were investigated by two-dimensional speckle tracking echocardiography, percentiles were created addressing the amount and time-to-peak...

Given a finite nonincreasing sequence of positive numbers a1 ≥ a2 ≥ . . . ≥ an > 0, select index j such that the absolute value of the difference between the sum of the first j terms and the sum of the remaining n− j terms is minimized. An analysis shows that the ratio of these two sums is then bounded between γ ≡ max{2, β} and 1/γ, where β is the maximum pairwise ratio of successive terms in t...