Recognizing When a Preference System is Close to Admitting a Master List

A preference system $$\mathcal {I}$$ is an undirected graph where vertices have preferences over their neighbors, and admits a master list if all can be derived from single ordering vertices. We study the problem of deciding whether given close to admitting based on three different distance measures. determine computational complexity following questions: modified by (i) k swaps in preferences, (ii) edge deletions, or (iii) vertex deletions so that resulting instance list? investigate these problems detail viewpoint parameterized approximation. also present two applications related stable popular matchings.