In this paper, we present two algorithms to obtain the convex hull of a set of points that are stored in the compact data structure called \(k^2\)-\(tree\). This problem consists in given a set of points P in the Euclidean space obtaining the smallest convex region (polygon) containing P. Traditional algorithms to compute the convex hull do not scale well for large databases, such as spatial databases, since the data does not reside in main memory. We use the \(k^2\)-\(tree\) compact data structure to represent, in main memory, efficiently a binary adjacency matrix representing points over a 2D space. This structure allows an efficient navigation in a compressed form. The experimentations performed over synthetical and real data show that our proposed algorithms are more efficient. In fact they perform over four order of magnitude compared with algorithms with time complexity of \(O(n \log n)\).

在本文中，我们提出两种算法来获取一组点的凸包，这些点存储在称为\（k ^ 2 \） - \（tree \）的紧凑数据结构中。这个问题在于给定欧氏空间中的一组点P，以获得包含P的最小凸区域（多边形）。对于大型数据库（例如空间数据库）而言，计算凸包的传统算法无法很好地扩展，因为数据不会驻留在主内存中。我们使用\（k ^ 2 \） - \（tree \）紧凑的数据结构，以便在主存储器中高效地表示二进制邻接矩阵，该矩阵表示2D空间上的点。这种结构允许以压缩形式进行有效导航。对综合数据和真实数据进行的实验表明，我们提出的算法效率更高。实际上，与时间复杂度为\（O（n \ log n）\）的算法相比，它们执行了四个数量级。