Balanced Connected Subgraph Problem in Geometric Intersection Graphs

Sujoy Bhore, Satyabrata Jana, Supantha Pandit, Sasanka Roy

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


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.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 13th International Conference, COCOA 2019, Proceedings
EditorsYingshu Li, Mihaela Cardei, Yan Huang
Number of pages13
ISBN (Print)9783030364113
StatePublished - 1 Jan 2019
Externally publishedYes
Event13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019 - Xiamen, China
Duration: 13 Dec 201915 Dec 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11949 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019


  • Balanced connected subgraph
  • Circular-arc graphs
  • Color-balanced
  • Fixed parameter tractable
  • Interval graphs
  • NP-hard
  • Outer-string graphs
  • Permutation graphs
  • Unit-disk graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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