Untangling Tanglegrams: Comparing Trees by Their Drawings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Exact bipartite crossing minimization under tree constraints
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Note: A note on the parameterized complexity of unordered maximum tree orientation
Discrete Applied Mathematics
Satisfying more than half of a system of linear equations over GF(2): A multivariate approach
Journal of Computer and System Sciences
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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(2 k 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).