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The quest for efficient sorting is ongoing, and we will explore a graph-basedstable sorting strategy, in particular employing comparison graphs. We use thetopological sort to map the comparison graph to a linear domain, and we canmanipulate our graph such that the resulting topological sort is the sortedarray. By taking advantage of the many relations between Hamiltonian paths andtopological sorts in comparison graphs, we design a Divide-and-Conqueralgorithm that runs in the optimal $O(n \log n)$ time. In the process, weconstruct a new merge process for graphs with relevant invariant properties forour use. Furthermore, this method is more space-efficient than the famous {\scMergeSort} since we modify our fixed graph only.

Sorting an Array Using the Topological Sort of a Corresponding Comparison Graph