weberknecht -- a One-Sided Crossing Minimization solver
Johannes Rauch
TL;DR
The paper tackles One-Sided Crossing Minimization for bipartite two-layer drawings by introducing weberknecht, an exact solver, and weberknecht_h, a heuristic counterpart, both implemented in C++ and available on GitHub. It formulates the problem as a mixed-integer program over the ordering of $B$ with binary variables $x_{u,v}$ and employs data-reduction rules to shrink the search space before solving a reduced MIP via a custom branch-and-bound with lazy constraint generation, aided by HiGHS for LP subproblems. Key contributions include a comprehensive suite of data-reduction strategies (e.g., degree-zero vertex handling and cross-count based pruning) and an LP-guided branch-and-bound framework that avoids upfront enumeration of all $(n^3)$ constraints. The approach delivers practical exact and high-quality heuristic solutions for OSCM challenge instances, improving scalability and offering robust preprocessing to accelerate solving in graph-drawing applications.
Abstract
We describe the implementation of the exact solver weberknecht and the heuristic solver weberknecht_h for the One-Sided Crossing Minimization problem.