# Exact Bipartite Crossing Minimization under Tree Constraints

Baumann, Frank and Buchheim, Christoph and Liers, Frauke
(2010)
*Exact Bipartite Crossing Minimization under Tree Constraints.*
**Published In:**
9th International Symposium on Experimental Algorithms SEA 2010, Lecture Notes in Computer Science. 6049 Springer Verlag 2010, pp. 118-128.

## Abstract

A tanglegram consists of a pair of (not necessarily binary) trees T_1, T_2 with leaf sets L_1, L_2. Additional edges, called tangles, may connect nodes in L_1 with those in L_2. The task is to draw the tanglegram with a minimum number of tangle edge crossings while making sure that no crossing occurs between edges within each tree. This problem has relevant applications in computational biology, e.g., for the comparison of phylogenetic trees. In this work, we show that the problem can be formulated as a quadratic linear ordering problem (QLO) with additional side constraints. It was already shown that, appropriately reformulated, the QLO polytope is a face of some cut polytope. It turns out that the additional side constraints arising in our application do not destroy this property. Therefore, any polyhedral approach to max-cut can be used in our context. We present experimental results for drawing random and realistic tanglegrams using both linear and semidefinite programming techniques, showing that our approach is very efficient in practice.

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ZAIK Number: | zaik2009-581 |
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Depositing User: | Christoph Buchheim |

Date Deposited: | 26 Jul 2010 00:00 |

Last Modified: | 09 Jan 2012 12:12 |

URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/581 |