Splitting a variable in a Boolean formula means to replace an arbitrary set of its occurrences by a new variable. In the minimum splitting SAT problem, we ask for a minimum-size set of variables to be split in order to make the formula satisfiable. This problem is known to be APX-hard, even for 2-CNF formulas. We consider the case of 2CNF Horn formulas, i. e., 2-CNF formulas without positive 2-...

Approximation Algorithms for Clustering Clustering items into groups is a fundamental problem in the information sciences. Many typical clustering optimization problems are NP-hard and so cannot be expected to be solved optimally in a reasonable amount of time. Although the use of heuristics is common, in this dissertation we seek approximation algorithms, whose performance ratio in relation to...

Butman, Hermelin, Lewenstein, and Rawitz proved that CLIQUE in t-interval graphs is NP-hard for t ≥ 3. We strengthen this result to show that CLIQUE in 3-track interval graphs is APX-hard.

The study of the approximability properties of NP-hard optimization problems has recently made great advances mainly due to the results obtained in the field of proof checking. The last important breakthrough proves the APX-completeness of several important optimization problems and thus reconciles “two distinct views of approximation classes: syntactic and computational” [S. Khanna et al., in ...

Define Minimum Soapy Union (MinSU) as the following optimization problem: given a k-tuple (X1, X2, . . . , Xk) of finite integer sets, find a k-tuple (t1, t2, . . . , tk) of integers that minimizes the cardinality of (X1 + t1) ∪ (X2 + t2) ∪ · · · ∪ (Xn + tk). We show that MinSU is NP-complete, APX-hard, and polynomial for fixed k. MinSU appears naturally in the context of protein shotgun sequen...

Induction of decision trees is one of the most successful approaches to supervised machine learning. Branching programs are a generalization of decision trees and, by the boosting analysis, exponentially more eeciently learnable than decision trees. In experiments this advantage has not been seen to materialize. Decision trees are easy to simplify using pruning. For branching programs no such a...

Studies on physiological and biochemical processes in crops are highly relevant for breeders to produce hybrids with high yield. Two different maturity groups of maize were tested this study. The research site was located at the Látókép Experimental Station University Debrecen experiment lasted 2 years. examined nitrogen ranges separated into two parts. Firstly, effects fertilizer ranging from ...

Abstract The New Zealand Greenshell™ mussel ( Perna canaliculus ) supports the largest aquaculture industry in country. However, summer mortality events and potential disease outbreaks may threaten growth of this industry. As an approach to gauging threats through seasons, a detailed histopathological examination was conducted on 256 adult cultured mussels collected from farm between April 2018...

Abstract Apixaban (APX) is a novel anticoagulant drug used in the treatment of ischemic stroke and venous thromboembolism. In this study, two different chromatographic methods were developed for determination APX pharmaceutical products. first method, an Agilent C18 column (250 mm × 4.6 mm, 5 μm) was used, temperature kept constant at 30°C. The mobile phase chosen to be 0.1% trifluoroacetic aci...

Reactive oxygen species (ROS) are produced during seed desiccation, germination, and ageing, leading to cellular damage and seed deterioration and, therefore, decreased seed longevity. The effects of simultaneous over-expression of two antioxidant enzymes on seed longevity and seed germination under stressful conditions were investigated. Transgenic tobacco simultaneously over-expressing the Cu...