Chordal Editing is Fixed-Parameter Tractable - Cao, Yixin; Marx, Dániel (Algorithmica, 2016)
Graph modification problems typically ask for a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem that allows all three types of operations: given a graph and integers , and , the chordal editing problem asks whether can be transformed into a chordal graph by at most vertex deletions, edge deletions, and edge additions. Clearly, this problem generalizes both chordal deletion and chordal completion (also known as minimum fill - in ). Our main result is an algorithm for chordal editing in time , where and is the number of vertices of . Therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case chordal deletion .