The crossing angle of a straight-line drawing Γ of a graph G = (V, E) is the smallest angle between two crossing edges in Γ . Deciding whether a graph G has a straight-line drawing with a crossing angle of 90 • is N P-hard [1]. We propose a simple heuristic to compute a drawing with a large crossing angle. The heuristic greedily selects the best position for a single vertex in a random set of points. The algorithm is accompanied by a speed-up technique to compute the crossing angle of a straight-line drawing. We show the effectiveness of the heuristic in an extensive empirical evaluation. Our heuristic was clearly the winning algorithm (CoffeeVM) in the Graph Drawing Challenge 2017 [6].

Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose a fixed number of items from several disjoint sets, such that the worst-case costs after taking a recovery action are as small as possible. The uncertainty is modeled as a discrete budgeted set, where the adversary can increase the costs of a fixed number of items.While special cases of this problem have been studied before, its complexity has remained open. In this work we make several contributions towards closing this gap. We show that the problem is NP-hard and identify a special case that remains solvable in polynomial time. We provide a compact mixed-integer programming formulation and two additional extended formulations. Finally, computational results are provided that compare the efficiency of different exact solution approaches.

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