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INFORMS
2010

Exact Algorithms for the Quadratic Linear Ordering Problem

9 years 11 months ago
Exact Algorithms for the Quadratic Linear Ordering Problem
The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods. Key words: quadratic optimization, linear ordering, crossing minimization This work was partially supported ...
Christoph Buchheim, Angelika Wiegele, Lanbo Zheng
Added 05 Mar 2011
Updated 05 Mar 2011
Type Journal
Year 2010
Where INFORMS
Authors Christoph Buchheim, Angelika Wiegele, Lanbo Zheng
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