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The canonical optimization variant of the above decision problem is usually known as the Maximum-Cut Problem or Max-Cut and is defined as: Given a graph G, find a maximum cut. The optimization variant is known to be NP-Hard. The opposite problem, that of finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm.
Control volume and control volume & boundary faces (Figure 2) Create control volumes near the edges in such a way that the physical boundaries coincide with control volume boundaries (Figure 1). Assume a general nodal point 'P' for a general control volume. Adjacent nodal points to the East and West are identified by E and W respectively.
In graph theory, the graph bandwidth problem is to label the n vertices v i of a graph G with distinct integers so that the quantity {| () |:} is minimized (E is the edge set of G). [1] The problem may be visualized as placing the vertices of a graph at distinct integer points along the x -axis so that the length of the longest edge is ...
To view multiple windows in AOL Desktop Gold, you'll want to resize and position them appropriately on your screen. You can also save the window size and position for the next time you sign in to Desktop Gold. Open the window you want to resize or move. Click and drag the outside border of the window to modify its size.
The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem .
Many problems in graph algorithms may be solved efficiently on graphs of low pathwidth, by using dynamic programming on a path-decomposition of the graph. [10] For instance, if a linear ordering of the vertices of an n -vertex graph G is given, with vertex separation number w , then it is possible to find the maximum independent set of G in ...
A graphical user interface (GUI) showing various elements: radio buttons, checkboxes, and other elements. A graphical user interface, or GUI [a], is a form of user interface that allows users to interact with electronic devices through graphical icons and visual indicators such as secondary notation.
Since the clique problem is NP-complete, this polynomial-time many-one reduction shows that subgraph isomorphism is also NP-complete. [3] An alternative reduction from the Hamiltonian cycle problem translates a graph G which is to be tested for Hamiltonicity into the pair of graphs G and H, where H is a cycle having the same number of vertices ...