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 G and integers k 1 , k 2 , and k 3 , the chordal editing problem asks whether G can be transformed into a chordal graph by at most k 1 vertex deletions, k 2 edge deletions, and k 3 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 2 O(k log k) · n O(1) , where k := k 1 + k 2 + k 3 and n is the number of vertices of G. 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.
Cao and Marx REF study a generalization of Chordal Completion, where three operations are allowed: vertex deletion, edge addition, and edge deletion.
Chordal Editing is Fixed-Parameter Tractable
Algorithmica
Algorithmica
Mathematics Computer Science