Multilevel Planarity
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In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let G = (V, E) be a directed graph and let ℓ: V → P( Z) be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of G is a planar drawing of G such that the y-coordinate of each vertex v ∈ V is y(v) ∈ℓ(v), and each edge is drawn as a strictly y-monotone curve. We present linear-time algorithms for testing multilevel planarity of embedded graphs with a single source and of oriented cycles. Complementing these algorithmic results, we show that multilevel-planarity testing is NP-complete even in very restricted cases.
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