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Separator-based data reduction for signed graph balancing

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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.

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Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743, Jena, Germany

    Falk Hüffner, Nadja Betzler & Rolf Niedermeier

Authors
  1. Falk Hüffner
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  2. Nadja Betzler
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  3. Rolf Niedermeier
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Corresponding author

Correspondence to Falk Hüffner.

Additional information

A preliminary shorter version of this paper appeared under the title “Optimal edge deletions for signed graph balancing” in the Proceedings of the 6th Workshop on Experimental Algorithms (WEA 2007), June 6–8, 2007, Rome, Italy, vol. 4525 in Lecture Notes in Computer Science, pp. 297–310, Springer, 2007.

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Hüffner, F., Betzler, N. & Niedermeier, R. Separator-based data reduction for signed graph balancing. J Comb Optim 20, 335–360 (2010). https://doi.org/10.1007/s10878-009-9212-2

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