st-Orientations with Few Transitive Edges

The problem of orienting the edges an undirected graph such that resulting digraph is acyclic and has a single source s sink t long tradition in theory central to many drawing algorithms. Such orientation called st-orientation. We address computing st-orientations graphs with minimum number transitive edges. prove NP-hard general case. For planar we describe ILP model fast practice. experimentally show optimum solutions dramatically reduce respect unconstrained computed via classical st-numbering Moreover, focusing on popular algorithms apply st-orientation as preliminary step, reducing leads drawings are much more compact.