TY - GEN

T1 - Balanced Connected Subgraph Problem in Geometric Intersection Graphs

AU - Bhore, Sujoy

AU - Jana, Satyabrata

AU - Pandit, Supantha

AU - Roy, Sasanka

N1 - Funding Information:
S. Bhore—The author is supported by the Austrian Science Fund (FWF) grant P 31119.
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 -