TY - GEN
T1 - Minimization and parameterized variants of vertex partition problems on graphs
AU - Tamura, Yuma
AU - Ito, Takehiro
AU - Zhou, Xiao
N1 - Funding Information:
Funding Yuma Tamura: Partially supported by JSPS KAKENHI Grant Number JP20J11259, Japan. Takehiro Ito: Partially supported by JSPS KAKENHI Grant Numbers JP18H04091 and JP19K11814, Japan. Xiao Zhou: Partially supported by JSPS KAKENHI Grant Number JP19K11813, Japan.
Publisher Copyright:
© Yuma Tamura, Takehiro Ito, and Xiao Zhou.
PY - 2020/12
Y1 - 2020/12
N2 - Let Π1, Π2, . . ., Πc be graph properties for a fixed integer c. Then, (Π1, Π2, . . ., Πc)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V1, V2, . . ., Vc such that the subgraph induced by Vi satisfies the graph property Πi for every i ∈ {1, 2, . . ., c}. Minimization and parameterized variants of (Π1, Π2, . . ., Πc)-Partition have been studied for several specific graph properties, where the size of the vertex subset V1 satisfying Π1 is minimized or taken as a parameter. In this paper, we first show that the minimization variant is hard to approximate for any nontrivial additive hereditary graph properties, unless c = 2 and both Π1 and Π2 are classes of edgeless graphs. We then give FPT algorithms for the parameterized variant when restricted to the case where c = 2, Π1 is a hereditary graph property, and Π2 is the class of acyclic graphs.
AB - Let Π1, Π2, . . ., Πc be graph properties for a fixed integer c. Then, (Π1, Π2, . . ., Πc)-Partition is the problem of asking whether the vertex set of a given graph can be partitioned into c subsets V1, V2, . . ., Vc such that the subgraph induced by Vi satisfies the graph property Πi for every i ∈ {1, 2, . . ., c}. Minimization and parameterized variants of (Π1, Π2, . . ., Πc)-Partition have been studied for several specific graph properties, where the size of the vertex subset V1 satisfying Π1 is minimized or taken as a parameter. In this paper, we first show that the minimization variant is hard to approximate for any nontrivial additive hereditary graph properties, unless c = 2 and both Π1 and Π2 are classes of edgeless graphs. We then give FPT algorithms for the parameterized variant when restricted to the case where c = 2, Π1 is a hereditary graph property, and Π2 is the class of acyclic graphs.
KW - Approximability
KW - Feedback vertex set problem
KW - Fixed-parameter tractability
KW - Graph algorithms
KW - Vertex partition problem
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U2 - 10.4230/LIPIcs.ISAAC.2020.40
DO - 10.4230/LIPIcs.ISAAC.2020.40
M3 - Conference contribution
AN - SCOPUS:85100930242
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 401
EP - 4013
BT - 31st International Symposium on Algorithms and Computation, ISAAC 2020
A2 - Cao, Yixin
A2 - Cheng, Siu-Wing
A2 - Li, Minming
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 31st International Symposium on Algorithms and Computation, ISAAC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -