Abstract. Let G = (N,A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest s-t path (SP) problem in G and the maximum capacity s-t path (MCP) problem in G. Suppose that P* is a shortest s-t path in G with respect to a nonnegative distance vector c. For each arc e ∈ A, the lower...

A circular-arc model M = (C,A) is a circle C together with a collection A of arcs of C. If no arc is contained in any other then M is a proper circular-arc model, if every arc has the same length then M is a unit circular-arc model and if A satisfies the Helly Property then M is a Helly circular-arc model. A (proper) (unit) (Helly) circular-arc graph is the intersection graph of the arcs of a (...

Given a network with capacities and transit times on the arcs, the quickest flow problem asks for a “flow over time” that satisfies given demands within minimal time. In the setting of flows over time, flow on arcs may vary over time and the transit time of an arc is the time it takes for flow to travel through this arc. In most real-world applications (such as, e.g., road traffic, communicatio...

The shortest path problem (SPP) is one of the most important combinatorial optimization problems in graph theory due to its various applications. The uncertainty existing in the real world problems makes it difficult to determine the arc lengths exactly. The fuzzy set is one of the popular tools to represent and handle uncertainty in information due to incompleteness or inexactness. In most cas...

A novel pure penalty discontinuous Galerkin method is proposed for the geometrically nonlinear analysis of multilayered composite plates and shells, modelled via high-order refined theories. The approach allows to build different two-dimensional equivalent single layer structural models, which are obtained by expressing covariant components displacement field through-the-thickness Taylor’s poly...

We present in this paper a parallel execution model of arc-consistency for Constraint Satisfaction Problems (CSP), implemented on a scaleable MIMD distributed memory machine. We have adopted the indexical scheme, an adequate approach to arc-consistency for functional constraints. The CSP is partitioned into N partitions, which are executed in parallel on N processors. Each processor applies seq...

The phase-field fracture free-energy functional is non-convex with respect to the displacement and phase field. This results in a poor performance of conventional monolithic solvers like Newton–Raphson method. In order circumvent this issue, researchers opt for alternate minimization (staggered) solvers. Staggered are robust based simulations as sub-problems convex nature. Nevertheless, stagger...

In recent years, numerical heat and fluid flow models have provided significant insight into welding processes and welded materials that could not have been achieved otherwise. However, these calculations are complex and time consuming, and are unsuitable in situations where rapid calculations arc desired. A practical solution to this problem is to develop a neural network that is trained with ...