An aesthetic property prevalent in Lombardi's art work is that he tends to place many vertices on consecutive stretches of linear or circular segments that go across the whole drawings. This creates a metaphor of a "visual flow" across a drawing. Inspired by this property, we study the following problems for orthogonal drawings of planar graphs (see Fig. 1): 1. A minimum segment orthogonal drawing, or MSO-drawing, of a planar graph G is an orthogonal drawing of G with the minimum number of segments. 2. A minimum segment cover orthogonal drawing, or MSCO-drawing, of G is one with the smallest set of segments covering all vertices of G.
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