On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\Omega(k/ \log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.Comment: 19 pages, v3: additional detail

Magma Design Automation: Component placement on chips; the "holey cheese" problem.

The costs of the fabrication of a chip is partly determined by the wire length needed by the transistors to respect the wiring scheme. The transistors have to be placed without overlap into a prescribed configuration of blockades, i.e. parts of the chipthat are beforehand excluded from positioning by for example some other functional component, and holes, i.e. the remaining free area on the chip. A method to minimize the wire length when the free area is a simply connected domain has already been implemented by Magma, but the placement problem becomes much more complex when the free area is not a simply connected domain anymore, forming a ``holey cheese''. One of the approaches of the problem in this case is to first cluster the transistors into so-called macro's in such a way that closely interconnected transistors stay together, and that the macro's can be fit into the holes. One way to carry out the clustering is to use a graph clustering algorithm, the so-called Markov Cluster algorithm. Another way is to combine the placement method of Magma on a rectangular area of the same size as the total size of the holes, and a min cut-max flow algorithm to divide that rectangle into more or less rectangular macro's in such a way that as little wires as possible are cut. It is now possible to formulate the Quadratic Assignment Problem that remains after clustering the original problem to one with 100 up to 1000 macros. There exists a lot of literature on finding the global minimum of the costs, but nowadays computational possibilities are still too restrictive to find an optimal solution within a reasonable amount of time and computational memory. however, we believe it is possible to find a solution that leads to a acceptable local minimum of the costs

The Alcuin number of a graph and its connections to the vertex cover number

We consider a planning problem that generalizes Alcuin's river crossing problem to scenarios with arbitrary conflict graphs. This generalization leads to the so-called Alcuin number of the underlying conflict graph. We derive a variety of combinatorial, structural, algorithmical, and complexity theoretical results around the Alcuin number. Our technical main result is an NP-certificate for the Alcuin number. It turns out that the Alcuin number of a graph is closely related to the size of a minimum vertex cover in the graph, and we unravel several surprising connections between these two graph parameters. We provide hardness results and a fixed parameter tractability result for computing the Alcuin number. Furthermore we demonstrate that the Alcuin number of chordal graphs, bipartite graphs, and planar graphs is substantially easier to analyze than the Alcuin number of general graphs

Solving a system of linear diophantine equations with lower and upper bounds on the variables

We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector satisfying the system of diophantine equations, and a set of vectors belonging to the null-space of the constraint matrix. Due to basis reduction, all these vectors are relatively short. The next step is to branch on linear combinations of the null-space vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained diophantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good results on real-life data, and on instances from the literatur

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

Medication-related hospital admissions and readmissions in older patients: an overview of literature

Background The number of medication related hospital admissions and readmissions are increasing over the years due to the ageing population. Medication related hospital admissions and readmissions lead to decreased quality of life and high healthcare costs. Aim of the review To assess what is currently known about medication related hospital admissions, medication related hospital readmissions, their risk factors, and possible interventions which reduce medication related hospital readmissions. Method We searched PubMed for articles about the topic medication related hospital admissions and readmissions. Overall 54 studies were selected for the overview of literature. Results Between the different selected studies there was much heterogeneity in definitions for medication related admission and readmissions, in study population and the way studies were performed. Multiple risk factors are found in the studies for example: polypharmacy, comorbidities, therapy non adherence, cognitive impairment, depending living situation, high risk medications and higher age. Different interventions are studied to reduce the number of medication related readmission, some of these interventions may reduce the readmissions like the participation of a pharmacist, education programmes and transition-of-care interventions and the use of digital assistance in the form of Clinical Decision Support Systems. However the methods and the results of these interventions show heterogeneity in the different researches. Conclusion There is much heterogeneity in incidence and definitions for both medication related hospital admissions and readmissions. Some risk factors are known for medication related admissions and readmissions such as polypharmacy, older age and additional diseases. Known interventions that could possibly lead to a decrease in medication related hospital readmissions are spare being the involvement of a pharmacist, education programs and transition-care interventions the most mentioned ones although controversial results have been reported. More research is needed to gather more information on this topic

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

O letramento e o ensino de literatura mediados por jogos digitais educacionais

A partir da dificuldade nacompreensão de textos literáriosque alunos do ensino médio apresentam, geralmente associada a pouca valoração da leitura, desenvolveu-se uma pesquisa que explora o jogo digital como motivador do interesse pela leitura de obras pertencentes ao sistema literário brasileiro, bem como no desenvolvimento do letramento deste aluno. A pesquisa apresenta resultados ainda preliminares e dá-se por meio de revisão bibliográfica, análises quanti/qualitativas, a formação de grupos de estudo com alunos de nível médio em instituições de ensino técnico e tecnológico e a criação de um fórum de discussão disponibilizado em uma importante rede social. O emprego do jogo a ser desenvolvido apoia-se nos conceitos de aprendizagem significativa, em estudos sobre a formação social da mente, bem como no conceito de zona de desenvolvimento proximal. Os sistemas de regras, a jogabilidade e a dimensão estética do jogo serão os diferenciais abordados como elementos motivacionais do aluno/leitor.XI Workshop tecnología informática aplicada en educaciónRed de Universidades con Carreras en Informática (RedUNCI