TY - GEN

T1 - Balanced Independent and Dominating Sets on Colored Interval Graphs

AU - Bhore, Sujoy

AU - Haunert, Jan Henrik

AU - Klute, Fabian

AU - Li, Guangping

AU - Nöllenburg, Martin

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely f-Balanced Independent Set (f-BIS) and f-Balanced Dominating Set (f-BDS). Let G= (V, E) be an interval graph with a color assignment function γ:V→{1,…,k} that maps all vertices in G onto k colors. A subset of vertices S⊆ V is called f-balanced if S contains f vertices from each color class. In the f-BIS and f-BDS problems, the objective is to compute an independent set or a dominating set that is f-balanced. We show that both problems are NP-complete even on proper interval graphs. For the BIS problem on interval graphs, we design two FPT algorithms, one parameterized by (f, k) and the other by the vertex cover number of G. Moreover, for an optimization variant of BIS on interval graphs, we present a polynomial time approximation scheme (PTAS) and an O(nlog n) time 2-approximation algorithm.

AB - We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely f-Balanced Independent Set (f-BIS) and f-Balanced Dominating Set (f-BDS). Let G= (V, E) be an interval graph with a color assignment function γ:V→{1,…,k} that maps all vertices in G onto k colors. A subset of vertices S⊆ V is called f-balanced if S contains f vertices from each color class. In the f-BIS and f-BDS problems, the objective is to compute an independent set or a dominating set that is f-balanced. We show that both problems are NP-complete even on proper interval graphs. For the BIS problem on interval graphs, we design two FPT algorithms, one parameterized by (f, k) and the other by the vertex cover number of G. Moreover, for an optimization variant of BIS on interval graphs, we present a polynomial time approximation scheme (PTAS) and an O(nlog n) time 2-approximation algorithm.

UR - http://www.scopus.com/inward/record.url?scp=85101517856&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-67731-2_7

DO - 10.1007/978-3-030-67731-2_7

M3 - Conference contribution

AN - SCOPUS:85101517856

SN - 9783030677305

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 89

EP - 103

BT - SOFSEM 2021

A2 - Bureš, Tomáš

A2 - Dondi, Riccardo

A2 - Gamper, Johann

A2 - Guerrini, Giovanna

A2 - Jurdzinski, Tomasz

A2 - Pahl, Claus

A2 - Sikora, Florian

A2 - Wong, Prudence W.

PB - Springer Science and Business Media Deutschland GmbH

T2 - 47th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2021

Y2 - 25 January 2021 through 29 January 2021

ER -