Parameterized Local Search for Vertex Cover: When Only the Search Radius Is Crucial

A k-swap W for a vertex cover S of a graph G is a vertex set of size at most k such that S\u27 = (S ? W) ? (W ? S), the symmetric difference of S and W, is a vertex cover of G. If |S\u27| < |S|, then W is improving. In LS-Vertex Cover, one is given a vertex cover S of a graph G and wants to know if there is an improving k-swap for S in G. In applications of LS-Vertex Cover, k is a very small parameter that can be set by a user to determine the trade-off between running time and solution quality. Consequently, k can be considered to be a constant. Motivated by this and the fact that LS-Vertex Cover is W[1]-hard with respect to k, we aim for algorithms with running time ?^f(k) ? n^?(1) where ? is a structural graph parameter upper-bounded by n. We say that such a running time grows mildly with respect to ? and strongly with respect to k. We obtain algorithms with such a running time for ? being the h-index of G, the treewidth of G, or the modular-width of G. In addition, we consider a novel parameter, the maximum degree over all quotient graphs in a modular decomposition of G. Moreover, we adapt these algorithms to the more general problem where each vertex is assigned a weight and where we want to find a d-improving k-swap, that is, a k-swap which decreases the weight of the vertex cover by at least d

Перераспределительные эффекты налогов и трансфертов: опыт Китая

Устойчивый и быстрый экономический рост Китая в течение последних десятилетий привел не только к повышению уровня доходов на душу населения, но также и к серьезному разрыву в доходах отдельных категорий граждан. Основными инструментами государственной политики перераспределения доходов являются налоги и трансферты. В статье анализируется их влияние на перераспределение доходов. Исследование проводилось с использованием метода декомпозиции на основе данных обследования городских домашних хозяйств Китая в 2002-2009 гг., представленных Национальным бюро статистики Китая. Эмпирические результаты исследования указывают на то, что чистые трансферты из бюджета сокращают неравенство доходов среди городского населения, и этот положительный эффект со временем возрастает. Подробное изучение данного вопроса показывает, что и налоги, и трансферты играют позитивную роль в корректировке неравномерного распределения доходов. Трансферты влияют в основном на сокращение горизонтального неравенства и вносят более значительный вклад в корректировку ситуации, чем налоги, которые главным образом способствуют сокращению вертикального неравенства. В целом, совместный перераспределительный эффект персонального подоходного налога и взносов на социальное страхование носит благоприятный характер и может использоваться для перераспределения доходов. Трансферты резидентам из государственного бюджета, страхование вкладов, социальная помощь и страхование от безработицы также уменьшают неравенство, однако эффект последних двух мер очень слабый. Резервный фонд, напротив, увеличивает разрыв в доходах. Выводы, сделанные по результатам исследования могут быть использованы при дальнейшем реформировании распределения доходов и продвижении налоговой реформы, а также в совершенствовании системы социального обеспечения.China’s sustained high-speed several-decade-long economic growth has raised the level of per capita income, but also brought about a serious income gap. Taxes and public transfers are main policy governmental tools in the process of redistribution. This paper leads a comprehensive analysis of the impacts of taxes and transfers on income redistribution using decomposition method and is based on China’s Urban Household Survey Data (2002-2009) derived from the National Bureau of Statistics of China. The empirical results reveal that government’s net transfer reduces urban household’s increasing market income inequality, and the improvement effect increases with time. Taking a closer look, it shows that both tax and transfer play positive adjusting roles. Transfer’s contribution is relatively larger, reflected mainly in the improvement of horizontal equality, while tax’s effect is mainly reflected in vertical equality. On the whole, the combined redistribution effect of personal income tax and social insurance expenses from residents to government is positive, and can play a role in regulating the income redistribution. Endowment insurance, social relief and unemployment insurance reduce inequality in the transfers of government to residents, even though the last two items’ effects are very weak. In contrast, provident fund expands income gap. The conclusions reached in this paper will refer to the refinement of income distribution reform, promotion of tax reform, and improvement of the social security system

Acceleration of convergence characteristic of the ICCG method

The effectiveness of renumbering for the incomplete Cholesky conjugate gradient (ICCG) solver, which is usually applied to direct solvers, is examined quantitatively by analyzing 3D standard benchmark models. On an acceleration factor which is introduced to obtain convergence quickly, indices for determining the optimum value of the acceleration factor, which minimizes the number of iterations, are discussed. It is found that the renumbering is effective to use with the ICCG solver, and the solver using the acceleration factor gives a good convergence characteristic even in the case when the conventional solver fails to provide convergent solutions</p

Finger Search in Grammar-Compressed Strings

Grammar-based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. Given a grammar, the random access problem is to compactly represent the grammar while supporting random access, that is, given a position in the original uncompressed string report the character at that position. In this paper we study the random access problem with the finger search property, that is, the time for a random access query should depend on the distance between a specified index $f$, called the \emph{finger}, and the query index $i$. We consider both a static variant, where we first place a finger and subsequently access indices near the finger efficiently, and a dynamic variant where also moving the finger such that the time depends on the distance moved is supported. Let $n$ be the size the grammar, and let $N$ be the size of the string. For the static variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and subsequently accessing in $O(\log D)$ time, where $D$ is the distance between the finger and the accessed index. For the dynamic variant we give a linear space representation that supports placing the finger in $O(\log N)$ time and accessing and moving the finger in $O(\log D + \log \log N)$ time. Compared to the best linear space solution to random access, we improve a $O(\log N)$ query bound to $O(\log D)$ for the static variant and to $O(\log D + \log \log N)$ for the dynamic variant, while maintaining linear space. As an application of our results we obtain an improved solution to the longest common extension problem in grammar compressed strings. To obtain our results, we introduce several new techniques of independent interest, including a novel van Emde Boas style decomposition of grammars