Closure Problem - Closure Problem - Definition

Definition

In a directed graph G = (V, A), a set S of vertices is said to be closed if every successor of every vertex in S is also in S. Equivalently, S is closed if it has no outgoing edge.

It may be assumed without loss of generality that G is a directed acyclic graph. For, if it is not acyclic, each of its strongly connected components must either be entirely contained in or entirely disjoint from any closed set. Therefore, the closures of G are in one-to-one correspondence with the closures of the condensation of G, a directed acyclic graph that has one vertex for each strongly connected component of G. In weighted closure problems, one may set the weight of any vertex of the condensation to the sum of the weights of the vertices in the corresponding strongly connected component of G.

Read more about this topic:  Closure Problem, Closure Problem

Other articles related to "definition, definitions":

Sustainable Development - Definition
... the Brundtland Report, which included what is now one of the most widely recognised definitions "Sustainable development is development that meets the needs of the present without compromising the ability ... It offers an integrated vision and definition of strong sustainability ... It generates a more nuanced definition of sustainable development “the need to ensure a better quality of life for all, now and into the future, in a just ...
Pashtun People - Pashtuns Defined
... These three definitions may be described as the ethno-linguistic definition, the religious-cultural definition, and the patrilineal definition, respectively ...
Definition - In Medicine
... In medical dictionaries, definitions should to the greatest extent possible be simple and easy to understand, preferably even by the general public useful clinically or in related areas where the definition will be ...
Definition of Dietary Fiber
... of plants that resist human digestive enzymes, a definition that includes lignin and polysaccharides ... The definition was later changed to also include resistant starches, along with inulin and other oligosaccharides ... Official definition of dietary fiber differs a little among different institutions Organization (reference) Definition Institute of Medicine Dietary fiber consists of nondigestible carbohydrates and lignin that are ...
ESPN - High Definition
... ESPN launched its 720p high-definition simulcast, originally branded as ESPNHD, on March 20, 2001 ... shows, along with most live events on ESPN, use high definition ... from non-HD sources is presented in a standard definition, 43 format with stylized pillarboxes ...

Famous quotes containing the word definition:

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    ... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.
    George Eliot [Mary Ann (or Marian)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)