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Many practical applications demand additional restrictions on an admissible\udplanar embedding. In particular, constraints on the permitted (clockwise) order\udof the edges around a vertex, like so-called side constraints, abound.\udIn this paper, we introduce a set of hierarchical embedding constraints that\udalso comprises side constraints. We present linear time algorithms for testing\udif a graph is ec-planar, i.e., admits a planar embedding satisfying the\udgiven embedding constraints, as well as for computing such an embedding.\udMoreover, we characterize the set of all possible ec-planar embeddings and\udconsider the problem of finding a planar combinatorial embedding of a planar\udgraph such that an additional edge can be inserted with the minimum number of\udcrossings; we show that this problem can still be solved in linear time under\udthe additional restrictions of embedding constraints.\u

Planarity Testing and Optimal Edge Insertion with Embedding Constraints