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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| Vydané v: | Algorithmica Ročník 75; číslo 1; s. 118 - 137 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Springer US
01.05.2016
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| ISSN: | 0178-4617, 1432-0541 |
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| Abstract | 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
. |
|---|---|
| AbstractList | 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
. |
| Author | Marx, Dániel Cao, Yixin |
| Author_xml | – sequence: 1 givenname: Yixin surname: Cao fullname: Cao, Yixin organization: Department of Computing, Hong Kong Polytechnic University, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) – sequence: 2 givenname: Dániel surname: Marx fullname: Marx, Dániel email: dmarx@cs.bme.hu organization: Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) |
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| Cites_doi | 10.1002/net.3230240208 10.1016/0166-218X(88)90075-3 10.1016/0022-247X(70)90282-9 10.1016/j.orl.2003.10.009 10.1007/BF02992776 10.1007/s00453-008-9233-8 10.1016/S0012-365X(96)00161-6 10.1137/0208049 10.1016/S0166-218X(02)00242-1 10.1016/j.tcs.2005.10.008 10.1137/0602010 10.1137/0215075 10.1137/0910070 10.1016/0020-0190(96)00050-6 10.1016/S0166-218X(00)00391-7 10.1137/S0097539796303044 10.5486/PMD.1962.9.1-2.02 10.1007/978-3-662-47672-7_25 10.1145/2500119 10.1007/s00453-014-9904-6 10.1007/978-1-4471-5559-1 10.1016/0022-0000(80)90060-4 |
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| Keywords | Chordal deletion Parameterized computation Clique tree decomposition Chordal completion Chordal graph Graph modification problems Holes Simplicial vertex sets |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation |
| Title | Chordal Editing is Fixed-Parameter Tractable |
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