Determination of the regularity radius r∗ of interval matrices is known to be a NP-hard problem. In this paper, a method for determining r∗ is suggested whose numerical complexity is not a priori exponential. The method is based on an equivalent transformation of the original problem to the problem of determining the real maximum magnitude eigenvalue μ∗ of an associated interval generalized eig...

We prove that, given a closure function the smallest preimage of a closed set can be calculated in polynomial time in the number of closed sets. This confirms a conjecture of Albenque and Knauer and implies that there is a polynomial time algorithm to compute the convex hull-number of a graph, when all its convex subgraphs are given as input. We then show that computing if the smallest preimage...

The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and experimental results for CSP. In the theoretical part we present the hull approach, a combinatorial algorithm for solving a linear programming relaxation and prove that it runs in polynomial time in the case...

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are a number of methods available for finding the convex hull based on geometric calculations, such as, the distance between points, but do not address the tech...

We give linear and polynomial time algorithms for computing a minimum hull-set in distance-hereditary and chordal graphs respectively. Prior to our result a polynomial time algorithm was only known for sub-classes of considered graph classes. Our techniques allow us to give at the same time a linear time algorithm for computing a minimum geodetic set in distancehereditary graphs.

We discuss one known and five new interrelated methods for bounding the hull of the solution set of a system of interval linear equations. Each method involves a polynomial amount of computing; but requires considerably more effort than Gaussian elimination. However, each method can yield sharper results for appropriate problems. For certain problems, our methods can obtain sharp bounds for one...

We implement the finite-difference (FD) solver and the Hull-White (HW) tree for numerical treatment of the pricing problem under the Hull-White interest rate model. We find that the FD solver is superior to the HW tree.

We describe a common generalization of the weighted matching problem and the weighted matroid intersection problem. In this context we establish common generalizations of the main results on those two problems|polynomial-time solvability, min-max theorems, and totally dual integral polyhedral descriptions. New applications of these results include a strongly polynomial separation algorithm for ...

In this paper we address the problem of computing a minimal H-representation of the convex hull of the union of k H-polytopes in R. Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto the two-dimensional space and solving a linear program. The resulting algorithm is polynomial in the...