Multidimensional Dominance Drawings and Their Applications

In a dominance drawing Γ of directed acyclic graph (DAG) G, vertex v is reachable from u if, and only if all the coordinates are greater than or equal to in Γ. Dominance drawings DAGs very important many areas research. They combine aspect DAG on grid with fact that transitive closure apparently obvious by relation between points associated vertices. The smallest number d for which given G has d-dimensional called dimension, it NP-hard compute. this paper, we present efficient algorithms computing dimensions respecting theoretical bounds. We first describe simple algorithm shows how compute its compressed closure. Next, more complicated algorithm, based concept modular decomposition obtaining lower dimensions. Finally, consider weak dominance, relaxed version discuss interesting experimental results.