It was previously known that neither Max Clique nor Min Chromatic Number can be approximated in polynomial time within n1− , for any constant > 0, unless NP = ZPP. In this paper, we extend the reductions used to prove these results and combine the extended reductions with a recent result of Samorodnitsky and Trevisan to show that unless NP ⊆ ZPTIME(2 logn) 3/2)), neither Max Clique nor Min Chro...

Given a system of constraints `i ≤ ai x ≤ ui, where ai ∈ {0, 1}, and `i, ui ∈ R+, for i = 1, . . . ,m, we consider the problem Mrfs of finding the largest subsystem for which there exists a feasible solution x ≥ 0. We present approximation algorithms and inapproximability results for this problem, and study some important special cases. Our main contributions are : 1. In the general case, where...

We consider the problem of scheduling n independent multiprocessor tasks with due dates and unit processing times, where the objective is to compute a schedule minimizing the throughput. We derive the complexity results and present several approximation algorithms. For the parallel variant of the problem, we introduce the first-fit increasing algorithm and the latest first increasing algorithm,...

Cubicity of a graph G is the smallest dimension d, for which G is a unit disc graph in R, under the l∞ metric, i.e. G can be represented as an intersection graph of d-dimensional (axis-parallel) unit hypercubes. We call such an intersection representation a d-dimensional cube representation of G. Computing cubicity is known to be inapproximable in polynomial time, within an O(n) factor for any ...

Boxicity of a graph G(V, E), denoted by box(G), is the minimum integer k such that G can be represented as the intersection graph of axis parallel boxes in R. The problem of computing boxicity is inapproximable even for graph classes like bipartite, co-bipartite and split graphs within O(n)-factor, for any ǫ > 0 in polynomial time unless NP = ZPP . We give FPT approximation algorithms for compu...

We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G−B), where B are the bridges of G. In particular, it follows that for strongly chordal graphs and so-called power chordal graphs the injective chromatic number can be determined in polynomial time. Moreover, for chordal graphs in general, we show ...

OBJECTIVES Several studies have confirmed the high potential of the forced oscillation technique for the assessment of respiratory modifications related to chronic obstructive pulmonary disease. However, most of these studies did not employ within-breath analyses of the respiratory system. The aim of this study is to analyze respiratory impedance alterations in different phases of the respirato...

Dobrobit životinja se u EU promiče zadnjih četrdesetak godina dok je Hrvatskoj veći značaj dobila 2018. godine početkom provedbe Mjere 14 (M14). M14 podržava više standarde uzgoju stoke od uobičajenih iz četiri područja dobrobiti (poboljšana hranidba, poboljšani uvjeti smještaja, pristup na otvoreno, poboljšana skrb) za pet stočarskih sektora: govedarstvo, svinjogojstvo, peradarstvo, kozarstvo ...

OBJECTIVE Menstrual disorders are common in young women, and heavy menstrual blood losses (MBL) are an important cause of anaemia. Menstrual morbidity normally goes untreated in developing countries where cultural barriers also serve to mask the problems. We investigated the prevalence of menstrual morbidity, and measured MBL and its relationship to iron deficiency in a rural adolescent populat...

Previous reports have shown that blood lead levels in humans are associated with a polymorphic form of delta-aminolevulinate dehydratase (ALAD), an enzyme of heme biosynthesis that binds and is inhibited by lead. We hypothesized that ALAD levels may influence the distribution and accumulation of lead in the blood and target organs. To assess this, we studied strains of mice that differ in the n...