TY - GEN

T1 - The balanced connected subgraph problem

AU - Bhore, Sujoy

AU - Chakraborty, Sourav

AU - Jana, Satyabrata

AU - Mitchell, Joseph S.B.

AU - Pandit, Supantha

AU - Roy, Sasanka

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following Balanced Connected Subgraph (shortly, BCS) problem. The input is a graph G = (V, E), with each vertex in the set V having an assigned color, "red" or "blue". We seek a maximum-cardinality subset (Formula presented) of vertices that is color-balanced (having exactly |V′|/2 red nodes and |V′|/2 blue nodes), such that the subgraph induced by the vertex set V′ in G is connected. We show that the BCS problem is NP-hard, even for bipartite graphs G (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem for various classes of the input graph G, including, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue 2-coloring, and graphs with diameter 2. For each of these classes either we prove NP-hardness or design a polynomial time algorithm.

AB - The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following Balanced Connected Subgraph (shortly, BCS) problem. The input is a graph G = (V, E), with each vertex in the set V having an assigned color, "red" or "blue". We seek a maximum-cardinality subset (Formula presented) of vertices that is color-balanced (having exactly |V′|/2 red nodes and |V′|/2 blue nodes), such that the subgraph induced by the vertex set V′ in G is connected. We show that the BCS problem is NP-hard, even for bipartite graphs G (with red/blue color assignment not necessarily being a proper 2-coloring). Further, we consider this problem for various classes of the input graph G, including, e.g., planar graphs, chordal graphs, trees, split graphs, bipartite graphs with a proper red/blue 2-coloring, and graphs with diameter 2. For each of these classes either we prove NP-hardness or design a polynomial time algorithm.

KW - Balanced connected subgraph

KW - Bipartite graphs

KW - Chordal graphs

KW - Color-balanced

KW - NP-hard

KW - Planar graphs

KW - Split graphs

KW - Trees

UR - http://www.scopus.com/inward/record.url?scp=85063500083&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11509-8_17

DO - 10.1007/978-3-030-11509-8_17

M3 - Conference contribution

AN - SCOPUS:85063500083

SN - 9783030115081

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

SP - 201

EP - 215

BT - Algorithms and Discrete Applied Mathematics - 5th International Conference, CALDAM 2019, Proceedings

A2 - Vijayakumar, Ambat

A2 - Pal, Sudebkumar Prasant

PB - Springer Verlag

T2 - 5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019

Y2 - 14 February 2019 through 16 February 2019

ER -