Chordal Editing is Fixed-Parameter Tractable
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...
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| Vydáno v: | Algorithmica Ročník 75; číslo 1; s. 118 - 137 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.05.2016
|
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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
. |
|---|---|
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-015-0014-x |