Construct, Merge, Solve and Adapt: Application to the repetition-free longest common subsequence problem

In this paper we present the application of a recently proposed, general, algorithm for combinatorial optimization to the repetition-free longest common subsequence problem. The applied algorithm, which is labelled Construct, Merge, Solve & Adapt, generates sub-instances based on merging the solution components found in randomly constructed solutions. These sub-instances are subsequently solved by means of an exact solver. Moreover, the considered sub-instances are dynamically changing due to adding new solution components at each iteration, and removing existing solution components on the basis of indicators about their usefulness. The results of applying this algorithm to the repetition-free longest common subsequence problem show that the algorithm generally outperforms competing approaches from the literature. Moreover, they show that the algorithm is competitive with CPLEX for small and medium size problem instances, whereas it outperforms CPLEX for larger problem instances.Peer ReviewedPostprint (author's final draft

Solving Medium-Density Subset Sum Problems in Expected Polynomial Time: An Enumeration Approach

The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio of $n$ to $m$, where $m$ is the logarithm of the largest integer within $A$. Based on the structural and statistical properties of subset sums, we present an improved enumeration scheme for SSP, and implement it as a complete and exact algorithm (EnumPlus). The algorithm always equivalently reduces an instance to be low-density, and then solve it by enumeration. Through this approach, we show the possibility to design a sole algorithm that can efficiently solve arbitrary density instance in a uniform way. Furthermore, our algorithm has considerable performance advantage over previous algorithms. Firstly, it extends the density scope, in which SSP can be solved in expected polynomial time. Specifically, It solves SSP in expected $O(n\log{n})$ time when density $d \geq c\cdot \sqrt{n}/\log{n}$, while the previously best density scope is $d \geq c\cdot n/(\log{n})^{2}$. In addition, the overall expected time and space requirement in the average case are proven to be $O(n^5\log n)$ and $O(n^5)$ respectively. Secondly, in the worst case, it slightly improves the previously best time complexity of exact algorithms for SSP. Specifically, the worst-case time complexity of our algorithm is proved to be $O((n-6)2^{n/2}+n)$, while the previously best result is $O(n2^{n/2})$.Comment: 11 pages, 1 figur

Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

Exact Cover with light

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.Comment: 20 pages, 4 figures, New Generation Computing, accepted, 200

Smoking among morbidly obese patients

<p>Abstract</p> <p>Background</p> <p>Smokers usually have a lower Body Mass Index (BMI) when compared to non-smokers. Such a relationship, however, has not been fully studied in obese and morbidly obese patients. The objective of this study was to evaluate the relationship between smoking and BMI among obese and morbidly obese subjects.</p> <p>Methods</p> <p>In a case-control study design, 1022 individuals of both genders, 18-65 years of age, were recruited and grouped according to their smoking status (smokers, ex-smokers, and non-smokers) and nutritional state according to BMI (normal weight, overweight, obese, and morbidly obese).</p> <p>Results</p> <p>No significant differences were detected in the four BMI groups with respect to smoking status. However, there was a trend towards a higher frequency of smokers among the overweight, obese, and morbidly obese subjects compared to normal weight individuals (p = 0.078). In a logistic regression, after adjusting for potential confounders, morbidly obese subjects had an adjusted OR of 2.25 (95% CI, 1.52-3.34; p < 0.001) to be a smoker when compared to normal weight individuals.</p> <p>Discussion</p> <p>In this sample, while the frequency of smokers diminished in normal weight subjects as the BMI increased, such a trend was reversed in overweight, obese, and morbidly obese patients. In the latter group, the prevalence of smokers was significantly higher compared to the other groups. A patient with morbid obesity had a 2-fold increased risk of becoming a smoker. We speculate that these finding could be a consequence of various overlapping risk behaviors because these patients also are generally less physically active and prefer a less healthy diet, in addition to having a greater alcohol intake in relation to their counterparts. The external validity of these findings must be confirmed.</p

Social disconnectedness, loneliness, and mental health among adolescents in Danish high schools : a nationwide cross-sectional study

Background: Previous research has suggested that social disconnectedness experienced at school is linked to mental health problems, however, more research is needed to investigate (1) whether the accumulation of various types of social disconnectedness is associated with risk for mental health problems, and (2) whether loneliness is a mechanism that explains these associations. Methods: Using data from the Danish National Youth Study 2019 (UNG19), nation-wide cross-sectional data from 29,086 high school students in Denmark were analyzed to assess associations between social disconnectedness experienced at school (lack of classmate support, lack of teacher support, lack of class social cohesion, and not being part of the school community) and various mental health outcomes, as well as the mediating role of loneliness for each type of disconnectedness. Multilevel regression analyses were conducted to assess the associations. Results: Descriptive analyses suggest that 27.5% of Danish high school students experience at least one type of social disconnectedness at school. Each type of social disconnectedness was positively associated with mental health problems (depression symptoms, anxiety symptoms, stress, sleep problems, suicidal ideation, non-suicidal self-injury, eating disorder, body dissatisfaction, and low self-esteem) and negatively associated with mental well-being. In all cases, loneliness significantly mediated the associations. We found a clear dose-response pattern, where each addition in types of social disconnectedness was associated with (1) stronger negative coefficients with mental well-being and (2) stronger positive coefficients with mental health problems. Conclusion: Our results add to a large evidence-base suggesting that mental health problems among adolescents may be prevented by promoting social connectedness at school. More specifically, fostering social connectedness at school may prevent loneliness, which in turn may promote mental well-being and prevent mental health problems during the developmental stages of adolescence. It is important to note that focusing on single indicators of school social connectedness/disconnectedness would appear to be insufficient. Implications for practices within school settings to enhance social connectedness are discussed