论文标题
使用相应的比较图对数组进行排序
Sorting an Array Using the Topological Sort of a Corresponding Comparison Graph
论文作者
论文摘要
对有效排序的寻求正在进行中，我们将探索基于图的稳定排序策略，特别是采用比较图。我们使用拓扑排序将比较图映射到线性域，我们可以操纵我们的图形，以使所得的拓扑排序是排序的阵列。通过利用汉密尔顿路径与拓扑状态之间的许多关系，我们设计了一种以最佳$ o（n \ log n）$时间运行的分隔和诱导算法。在此过程中，我们构建了一个新的合并过程，用于具有相关不变属性的图形。此外，由于我们仅修改固定图，因此此方法比著名的{\ sc Mergesort}更为空间。
The quest for efficient sorting is ongoing, and we will explore a graph-based stable sorting strategy, in particular employing comparison graphs. We use the topological sort to map the comparison graph to a linear domain, and we can manipulate our graph such that the resulting topological sort is the sorted array. By taking advantage of the many relations between Hamiltonian paths and topological sorts in comparison graphs, we design a Divide-and-Conquer algorithm that runs in the optimal $O(n \log n)$ time. In the process, we construct a new merge process for graphs with relevant invariant properties for our use. Furthermore, this method is more space-efficient than the famous {\sc MergeSort} since we modify our fixed graph only.
