TY - GEN

T1 - Parameterized complexity classification of deletion to list matrix-partition for low-order matrices

AU - Agrawal, Akanksha

AU - Kolay, Sudeshna

AU - Madathil, Jayakrishnan

AU - Saurabh, Saket

N1 - Publisher Copyright:
© Akanksha Agrawal, Sudeshna Kolay, Jayakrishnan Madathil, and Saket Saurabh; licensed under Creative Commons License CC-BY

PY - 2019/12/1

Y1 - 2019/12/1

N2 - Given a symmetric ` × ` matrix M = (mi,j) with entries in {0, 1, ∗}, a graph G and a function L : V (G) → 2[`] (where [`] = {1, 2, . . ., `}), a list M-partition of G with respect to L is a partition of V (G) into ` parts, say, V1, V2, . . ., V` such that for each i, j ∈ {1, 2, . . ., `}, (i) if mi,j = 0 then for any u ∈ Vi and v ∈ Vj, uv ∈/ E(G), (ii) if mi,j = 1 then for any (distinct) u ∈ Vi and v ∈ Vj, uv ∈ E(G), (iii) for each v ∈ V (G), if v ∈ Vi then i ∈ L(v). We consider the Deletion to List M-Partition problem that takes as input a graph G, a list function L : V (G) → 2[`] and a positive integer k. The aim is to determine whether there is a k-sized set S ⊆ V (G) such that G − S has a list M-partition. Many important problems like Vertex Cover, Odd Cycle Transversal, Split Vertex Deletion, Multiway Cut and Deletion to List Homomorphism are special cases of the Deletion to List M-Partition problem. In this paper, we provide a classification of the parameterized complexity of Deletion to List M-Partition, parameterized by k, (a) when M is of order at most 3, and (b) when M is of order 4 with all diagonal entries belonging to {0, 1}.

AB - Given a symmetric ` × ` matrix M = (mi,j) with entries in {0, 1, ∗}, a graph G and a function L : V (G) → 2[`] (where [`] = {1, 2, . . ., `}), a list M-partition of G with respect to L is a partition of V (G) into ` parts, say, V1, V2, . . ., V` such that for each i, j ∈ {1, 2, . . ., `}, (i) if mi,j = 0 then for any u ∈ Vi and v ∈ Vj, uv ∈/ E(G), (ii) if mi,j = 1 then for any (distinct) u ∈ Vi and v ∈ Vj, uv ∈ E(G), (iii) for each v ∈ V (G), if v ∈ Vi then i ∈ L(v). We consider the Deletion to List M-Partition problem that takes as input a graph G, a list function L : V (G) → 2[`] and a positive integer k. The aim is to determine whether there is a k-sized set S ⊆ V (G) such that G − S has a list M-partition. Many important problems like Vertex Cover, Odd Cycle Transversal, Split Vertex Deletion, Multiway Cut and Deletion to List Homomorphism are special cases of the Deletion to List M-Partition problem. In this paper, we provide a classification of the parameterized complexity of Deletion to List M-Partition, parameterized by k, (a) when M is of order at most 3, and (b) when M is of order 4 with all diagonal entries belonging to {0, 1}.

KW - Almost 2-SAT

KW - Important separators

KW - Iterative compression

KW - List matrix partitions

KW - Parameterized classification

UR - http://www.scopus.com/inward/record.url?scp=85076346520&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2019.41

DO - 10.4230/LIPIcs.ISAAC.2019.41

M3 - Conference contribution

AN - SCOPUS:85076346520

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 30th International Symposium on Algorithms and Computation, ISAAC 2019

A2 - Lu, Pinyan

A2 - Zhang, Guochuan

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 30th International Symposium on Algorithms and Computation, ISAAC 2019

Y2 - 8 December 2019 through 11 December 2019

ER -