2 research outputs found
Multilevel Planarity
In this paper, we introduce and study multilevel planarity, a generalization of upward planarity and level planarity. Let be a directed graph and let be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of is a planar drawing of such that for each vertex its -coordinate is in , nd each edge is drawn as a strictly -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