TY - GEN
T1 - Balanced Connected Subgraph Problem in Geometric Intersection Graphs
AU - Bhore, Sujoy
AU - Jana, Satyabrata
AU - Pandit, Supantha
AU - Roy, Sasanka
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We study the (shortly,) problem on geometric intersection graphs such as interval, circular-arc, permutation, unit-disk, outer-string graphs, etc. Given agraph, where each vertex in V is colored with either “” or “”, the BCS problem seeks a maximum cardinality induced connected subgraph H of G such that H is, i.e., H contains an equal number of red and blue vertices. We study the computational complexity landscape of the BCS problem while considering geometric intersection graphs. On one hand, we prove that the BCS problem is NP-hard on the unit disk, outer-string, complete grid, and unit square graphs. On the other hand, we design polynomial-time algorithms for the BCS problem on interval, circular-arc and permutation graphs. In particular, we give algorithms for theproblem on both interval and circular-arc graphs, and those algorithms are used as subroutines for solving the BCS problem on the same classes of graphs. Finally, we present a FPT algorithm for the BCS problem on general graphs.
AB - We study the (shortly,) problem on geometric intersection graphs such as interval, circular-arc, permutation, unit-disk, outer-string graphs, etc. Given agraph, where each vertex in V is colored with either “” or “”, the BCS problem seeks a maximum cardinality induced connected subgraph H of G such that H is, i.e., H contains an equal number of red and blue vertices. We study the computational complexity landscape of the BCS problem while considering geometric intersection graphs. On one hand, we prove that the BCS problem is NP-hard on the unit disk, outer-string, complete grid, and unit square graphs. On the other hand, we design polynomial-time algorithms for the BCS problem on interval, circular-arc and permutation graphs. In particular, we give algorithms for theproblem on both interval and circular-arc graphs, and those algorithms are used as subroutines for solving the BCS problem on the same classes of graphs. Finally, we present a FPT algorithm for the BCS problem on general graphs.
KW - Balanced connected subgraph
KW - Circular-arc graphs
KW - Color-balanced
KW - Fixed parameter tractable
KW - Interval graphs
KW - NP-hard
KW - Outer-string graphs
KW - Permutation graphs
KW - Unit-disk graphs
UR - http://www.scopus.com/inward/record.url?scp=85078526147&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-36412-0_5
DO - 10.1007/978-3-030-36412-0_5
M3 - Conference contribution
AN - SCOPUS:85078526147
SN - 9783030364113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 56
EP - 68
BT - Combinatorial Optimization and Applications - 13th International Conference, COCOA 2019, Proceedings
A2 - Li, Yingshu
A2 - Cardei, Mihaela
A2 - Huang, Yan
PB - Springer
T2 - 13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019
Y2 - 13 December 2019 through 15 December 2019
ER -