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 -