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 - https://www.scopus.com/pages/publications/85063500083
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 -