This paper tackles a generalization of the weight constrained shortest path problem in a directed network (WCSPP) in which replenishment arcs, that reset the accumulated weight along the path to zero, appear in the network. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests, and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we introduce the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We provide the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications.

No abstract

No abstract

No abstract

No abstract

We consider the variant of the shortest path problem in which a given set of paths is forbidden to occur as a subpath in an optimal path. We establish that the most-efficient algorithm for its solution, a dynamic programming algorithm, has polynomial time complexity; it had previously been conjectured that the algorithm has pseudo-polynomial time complexity. Furthermore, we show that this algorithm can be extended, without increasing its time complexity, to handle non elementary forbidden paths.

Virtual fractional flow reserve (vFFR) is an emerging technology employing patient-specific computational fluid dynamics (CFD) simulations to infer the hemodynamic significance of a coronary stenosis. Patient-specific boundary conditions are an important aspect of this approach and while most efforts make use of lumped parameter models to capture key phenomena, they lack the ability to specify the associated parameters on a patient-specific basis. When applying vFFR in a catheter laboratory setting using X-ray angiograms as the basis for creating the simulations, there is some indirect functional information available through the observation of the radio-opaque contrast agent motion. In this work, we present a novel method for tuning the lumped parameter arterial resistances (commonly incorporated in such simulations), based on simulating the physics of the contrast motion and comparing the observed and simulated arrival times of the contrast front at key points within a coronary tree. We present proof of principle results on a synthetically generated coronary tree comprised of multiple segments, demonstrating that the method can successfully optimize the arterial resistances to reconstruct the underlying velocity and pressure fields, providing a potential new means to improve the patient specificity of simulation-based technologies in this area.

No abstract