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In 1966 Ivan E. Sutherland listed 10 unsolved problems in computer graphics. [3] Problem number seven was "hidden-line removal". In terms of computational complexity, this problem was solved by Frank Devai in 1986. [4] Models, e.g. in computer-aided design, can have thousands or millions of edges. Therefore, a computational-complexity approach ...
edge cut A set of edge s whose removal disconnects the graph. A one-edge cut is called a bridge, isthmus, or cut edge. edge set The set of edges of a given graph G, sometimes denoted by E(G). edgeless graph The edgeless graph or totally disconnected graph on a given set of vertices is the graph that has no edges. It is sometimes called the ...
A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
Some modern desktop publishing programs, such as Adobe InDesign, evaluate the effects of all the different possible line-break choices on the entire paragraph, to choose the one that creates the least variance from the ideal spacing while justifying the lines (so as to reduce rivers); this also gives the least uneven edge when set with a ragged ...
The result of the classification determines the edges intersected by the line p. The algorithm is simple, easy to implement and extensible to a convex window as well. The line or line segment p can be computed from points r 1, r 2 given in homogeneous coordinates directly using the cross product as p = r 1 × r 2 = (x 1, y 1, w 1) × (x 2, y 2 ...
A graph and two of its cuts. The dotted line in red is a cut with three crossing edges. The dashed line in green is a min-cut of this graph, crossing only two edges. In computer science and graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David Karger and first ...
This hypergraph has order 7 and size 4. Here, edges do not just connect two vertices but several, and are represented by colors. Alternative representation of the hypergraph reported in the figure above, called PAOH. [1] Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left.
Each edge xy between two nodes of the SPQR tree is associated with two directed virtual edges, one of which is an edge in G x and the other of which is an edge in G y. Each edge in a graph G x may be a virtual edge for at most one SPQR tree edge. An SPQR tree T represents a 2-connected graph G T, formed as follows.