The geometric kernel (or simply the kernel) of a polyhedron is set points from which whole visible. Whilst computation polygon has been largely addressed in literature, fewer methods have proposed for polyhedra. most acknowledged solution estimation to solve linear programming problem. We present approach that extends and optimizes our previous method (Sorgente, 2021). Experimental results show...

In general, it is difficult to enumerate all vertices of a polytope in polynomial time. Here we present a polynomial algorithm which enumerates all vertices of a submodular base polyhedron in O(n31V)) time and in 0 ( n 2 ) space, where V is the vertex set of a base polyhedron and n the dimension of the underlying Euclidean space. Our algorithm is also polynomial delay, and a generalization of s...

This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity ...

Linear programs are problems that involve the optimization of a linear objective function subject to linear constraints. Every linear program has an inherent geometric representation. Each constraint defines an halfspace and the feasible region of the the linear program is the convex polyhedron defined by intersection of all the halfspaces. The maximal solution to the linear program (if it exis...

We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than ~. The corresponding factor for the class of clique tree inequalities is 8, while it i...

We study the mixed–integer knapsack polyhedron, that is, the convex hull of the mixed–integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet–defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalit...

A new method is suggested to compute the intersection of a set of direction cones encountered in the problem of passing a convex polyhedron through a window. The time requirement of this method is 0( nm), where n is the number of vertices of the polyhedron and m is the number of vertices of the window. Besides this time improvement, the concept of parallel congruence, which the new method is cr...