In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph.[1][2]
It may be solved in polynomial time using a reduction to the maximum flow problem. It may be used to model various application problems of choosing an optimal subset of tasks to perform, with dependencies between pairs of tasks, one example being in open pit mining.
^Ahuja, Ravindra K.; Magnanti, Thomas L.; Orlin, James B. (1993), "19.2 Maximum weight closure of a graph", Network flows, Englewood Cliffs, NJ: Prentice Hall Inc., pp. 719–724, ISBN 0-13-617549-X, MR 1205775.
^Cook, William J.; Cunningham, William H.; Pulleyblank, William R.; Schrijver, Alexander (2011), "Optimal closure in a digraph", Combinatorial Optimization, Wiley Series in Discrete Mathematics and Optimization, vol. 33, John Wiley & Sons, pp. 49–50, ISBN 9781118031391.
combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closureproblem is the task of finding the...
transitive closure. The closureproblem takes as input a vertex-weighted directed acyclic graph and seeks the minimum (or maximum) weight of a closure – a set...
part of the velocity. This is the closureproblem. Joseph Valentin Boussinesq was the first to attack the closureproblem, by introducing the concept of...
such that no edges leave C. The closureproblem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph...
problems that are polynomially-bounded. Assignment problem Bin packing problemClosureproblem Constraint satisfaction problem Cutting stock problem Dominating...
In mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive...
references or to create closures. There are two subtly different versions of the funarg problem. The upwards funarg problem arises from returning (or...
that, when considering the Gettier problem, the least counter-intuitive assumption we give up should be epistemic closure. Nozick suggested a "truth tracking"...
sound and consistent solutions, based on a K=3, 37-centre CP system: Closureproblem. Christaller's original scheme implies an infinite landscape. Although...
algorithm Closureproblem Generalized assignment problem Linear bottleneck assignment problem Quadratic assignment problem Stable marriage problem Andersen...
vertices outside the closure. For instance, a sink is a one-vertex closure. The closureproblem is the problem of finding a closure of minimum or maximum...
interest, for roughly the past century. The problem is recognized as a closureproblem, akin to the problem of closure in the BBGKY hierarchy. A transport equation...
directed graph Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest...
mountainous areas where rock slides and land slides create highway closureproblems. A rock shed is built over a roadway that is in the path of the slide...
with no edges that exit the subset, is called a closure. The closureproblem is the algorithmic problem of finding a dicut, in an edge-weighted directed...
circle-squaring problem, the pieces are typically required to be well-behaved. For instance, they may be restricted to being the closures of disjoint open...
a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of...
model must also have a random component cj= c+ cj’. This results in a closureproblem of infinite variables and equations and makes it impossible to solve...
introduction of the Tarski–Kuratowski algorithm; Kuratowski's closure-complement problem; Kuratowski's free set theorem; Kuratowski's intersection theorem;...
circle. That tendency to complete shapes and figures is called closure. The law of closure states that individuals perceive objects such as shapes, letters...
topics: Formal Structure Thematic Structure Special Terminal Features Problems of Closure Herrnstein Smith observes that regularity — such as the regular repetition...
In the philosophy of mind, the hard problem of consciousness is to explain why and how humans and other organisms have qualia, phenomenal consciousness...
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