An upward planar drawing of a digraph G is a planar drawing of G where every edge is drawn as a simple curve monotone in the vertical direction. A digraph is upward planar if it has an embedding that admits an upward planar drawing. The problem of testing whether a digraph is upward planar is NP-complete. In this paper we give a linear-time algorithm to test the upward planarity of a series-par...

An upward embedding of an embedded planar graph states, for ea h vertex v, whi h edges are in ident to v \above" or \below" and, in turn, indu es an upward orientation of the edges. In this paper we hara terize the set of all upward embeddings and orientations of a plane graph by using a simple ow model. We take advantage of su h a ow model to ompute upward orientations with the minimum number ...

A directed acyclic graph is upward planar if it allows a drawing without edge crossings where all edges are drawn as curves with monotonously increasing y-coordinates. The problem to decide whether a graph is upward planar or not is NP-complete in general, and while special graph classes are polynomial time solvable, there is not much known about solving the problem for general graphs in practi...

rade control structures are used to control bed erosion in steep small rivers mostly in the mountains. Scour downstream of this structure can lead to failure. Over the past years, the effect of different variables on this phenomena have been studied, however the effect of upward seepage which is common due to head difference of the banks water table or water surface level between the upstream a...