Over the past years there has been an enormous increase in the amount of data generated on a daily basis. A critical task in handling the information overload is locating the most interesting objects of a dataset according to a specific configuration or ranking function. Our work is based on the concept of dominance which compares data objects based on maximization preferences on the attribute values. Each data object is represented as a point in a multidimensional space based on its attribute values. The layers of maxima configuration assigns layer numbers to dataset points so that (some) points inside a layer dominate (some) points in subsequent layers and no point in a layer dominates another in the same layer. Furthermore, top-k dominating queries combine the merits of skyline (maxima) queries and top-k queries by returning the k first points with the highest dominance score, where the dominance score of an object is the number of objects it dominates. In this work we focus on 2-dimensional data and present, for the first time, algorithms and data structures with non-trivial asymptotic guarantees for maintaining the first k layers of maxima of a dataset under point insertions and deletions. Furthermore, we apply this solution in a sliding window problem setting, where one of the attributes is the insertion time of the object, and deletions always remove the oldest object. Finally, we tackle updates of arbitrary points in the semi-dynamic problem setting which permits point insertions and in the fully-dynamic problem setting which supports both point insertions and deletions. All of our solutions assume the word RAM model of computation. More precisely, the coordinates of each point are numbers that can be represented with w bits, where w is a parameter of the model (for example, in practice, usually $w=64$). All solutions require space linear with the number of points which is a crucial requirement for modern day applications.

在过去的几年中，每天生成的数据量已大大增加。处理信息超载的关键任务是根据特定的配置或排序功能定位数据集中最有趣的对象。我们的工作基于优势的概念，该概念根据属性值的最大化偏好来比较数据对象。每个数据对象都基于其属性值表示为多维空间中的一个点。最大值配置的图层将图层编号分配给数据集点，以使图层内的（某些）点主导后续图层中的（某些）点，而图层中的任何点都不主导同一图层中的另一个点。此外，前k个主导查询结合了天际线（最大值）查询和top-通过返回具有最高支配度得分的k个第一点来进行k个查询，其中对象的支配度得分是其支配的对象数。在这项工作中，我们专注于二维数据，并首次提出了具有非平凡渐近保证的算法和数据结构，用于维持前k个点插入和删除下数据集的最大值的各层。此外，我们在滑动窗口问题设置中应用此解决方案，其中属性之一是对象的插入时间，删除操作总是删除最旧的对象。最后，我们在允许点插入的半动态问题设置和同时支持点插入和删除的全动态问题设置中处理任意点的更新。我们所有的解决方案都采用word RAM计算模型。更准确地说，每个点的坐标是可以用w位表示的数字，其中w是模型的参数（例如，实际上，通常$w=64$）。所有解决方案都要求线性空间与点数成线性关系，这是现代应用程序的关键要求。