Abstract
Given two binary phylogenetic trees covering the same n species, it is useful to compare them by drawing them with leaves arranged side-by-side. To facilitate comparison, we would like to arrange the trees to minimize the number of crossings k induced by connecting pairs of identical species. This is the NP-hard Tanglegram Layout problem. By providing a fast transformation to the Balanced Subgraph problem, we show that the problem admits an O(2k n 4) algorithm, improving upon a previous fixed-parameter approach with running time O(c k n O(1)) where c ≈ 1000. We enhance a Balanced Subgraph implementation based on data reduction and iterative compression with improvements tailored towards these instances, and run experiments with real-world data to show the practical applicability of this approach. All practically relevant (k ≤ 1000) Tanglegram Layout instances can be solved exactly within seconds. Additionally, we provide a kernel-like bound by showing how to reduce the Balanced Subgraph instances for Tanglegram Layout on complete binary trees to a size of O(k logk).
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Böcker, S., Hüffner, F., Truss, A., Wahlström, M. (2009). A Faster Fixed-Parameter Approach to Drawing Binary Tanglegrams. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_3
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DOI: https://doi.org/10.1007/978-3-642-11269-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11268-3
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