Separator-based data reduction for signed graph balancing

Abstract Polynomial-time data reduction is a classical approach to hard graph problems. Typically, particular small subgraphs are replaced by smaller gadgets. We generalize this approach to handle any small subgraph that has a small separator connecting it to the rest of the graph. The problem we study is the NP-hard BALANCED SUBGRAPH problem, which asks for a 2-coloring of a graph that minimizes the inconsistencies with given edge labels. It has applications in social networks, systems biology, and integrated circuit design. The data reduction scheme unifies and generalizes a number of previously known data reductions, and can be applied to a large number of graph problems where a coloring or a subset of the vertices is sought. To solve the instances that remain after reduction, we use a fixed-parameter algorithm based on iterative compression with a very effective heuristic speedup. Our implementation can solve biological real-world instances exactly for which previously only appro...

• Type: Journal
• Year: 2010
• Where: JCO
• Authors: Falk Hüffner, Nadja Betzler, Rolf Niedermeier
• Keywords: Data Reductions, JCO 2010, Polynomial-time Data Reduction, Small Subgraph