Unit Interval Editing is Fixed-Parameter Tractable

Abstract

Given a graph \(G\) and integers \(k_1\), \(k_2\), and \(k_3\), the unit interval editing problem asks whether \(G\) can be transformed into a unit interval graph by at most \(k_1\) vertex deletions, \(k_2\) edge deletions, and \(k_3\) edge additions. We give an algorithm solving the problem in \(2^{O(k\log k)}\cdot (n+m)\) time, where \(k := k_1 + k_2 + k_3\), and \(n, m\) denote respectively the numbers of vertices and edges of \(G\). Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations.