Journal of Combinatorial Optimization

, Volume 20, Issue 4, pp 335–360 | Cite as

Separator-based data reduction for signed graph balancing

Article

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 approximations were known. In addition, we present experimental results for financial networks and random networks.

Keywords

Preprocessing Exact algorithm Parameterized algorithmics Algorithm engineering Gene-regulatory network Financial network 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Nadja Betzler
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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