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Sorting an Array Using the Topological Sort of a Corresponding Comparison Graph
Theoretical Computer Science ( IF 1.1 ) Pub Date : 2020-09-11 , DOI: 10.1016/j.tcs.2020.09.004
Balaram D. Behera

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(nlogn) 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 MergeSort since we modify our fixed graph only.



中文翻译:

使用相应比较图的拓扑排序对数组排序

对有效排序的追求正在进行中,我们将探索基于图的稳定排序策略,尤其是使用比较图。我们使用拓扑排序将比较图映射到线性域,并且可以操纵我们的图,以使生成的拓扑排序为排序数组。通过利用比较图中汉密尔顿路径与拓扑类别之间的许多关系,我们设计了一种在最优条件下运行的分而治之算法Øñ日志ñ时间。在此过程中,我们为具有相关不变属性的图构造了一个新的合并过程供我们使用。此外,此方法比著名的MergeSort更节省空间,因为我们仅修改了固定图。

更新日期:2020-09-11
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