Imbalance is fixed parameter tractable

Authors:
Daniel Lokshtanov;Neeldhara Misra;Saket Saurabh
Affiliations:
Department of Informatics, University of Bergen, Norway;Institute of Mathematical Sciences, Chennai, India;Institute of Mathematical Sciences, Chennai, India
Venue:
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Year:
2010

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Abstract

In the IMBALANCE MINIMIZATION problem we are given a graph G = (V,E) and an integer b and asked whether there is an ordering v1 . . . vn of V such that the sum of the imbalance of all the vertices is at most b. The imbalance of a vertex vi is the absolute value of the difference between the number of neighbors to the left and right of vi. The problem is also known as the BLALANCED VERTEX ORDERING problem and it finds many applications in graph drawing. We show that this problem is fixed parameter tractable and provide an algorithm that runs in time 2O(b log b) ċ nO(1). This resolves an open problem of Kára et al. [COCOON 2005].