6 research outputs found
On vertex adjacencies in the polytope of pyramidal tours with step-backs
We consider the traveling salesperson problem in a directed graph. The
pyramidal tours with step-backs are a special class of Hamiltonian cycles for
which the traveling salesperson problem is solved by dynamic programming in
polynomial time. The polytope of pyramidal tours with step-backs is
defined as the convex hull of the characteristic vectors of all possible
pyramidal tours with step-backs in a complete directed graph. The skeleton of
is the graph whose vertex set is the vertex set of and the
edge set is the set of geometric edges or one-dimensional faces of .
The main result of the paper is a necessary and sufficient condition for vertex
adjacencies in the skeleton of the polytope that can be verified in
polynomial time.Comment: in Englis
Order cones: A tool for deriving k-dimensional faces of cones of subfamilies of monotone games
In this paper we introduce the concept of order cone. This concept is inspired by the concept of order polytopes, a well-known object coming from Combinatorics. Similarly to order polytopes, order cones are a special type of polyhedral cones whose geometrical structure depends on the properties of a partially ordered set (brief poset). This allows to study these properties in terms of the subjacent poset, a problem that is usually simpler to solve. From the point of view of applicability, it can be seen that many cones appearing in the literature of monotone TU-games are order cones. Especially, it can be seen that the cones of monotone games with restricted cooperation are order cones, no matter the structure of the set of feasible coalitions