We tackle the problem of finding, for each network within a collection, shortest path between two given nodes, while not exceeding limits set shared resources. present an integer programming (IP) formulation this and propose parallelizable matheuristic consisting three phases: (1) generation feasible solutions, (2) combination (3) solution improvement. show that paths found with our procedure c...

The problem of nding a shortest path through a known environment has been well studied. A more realistic and challenging problem is navigation through an unknown environment, where path planning is implemented \on the y" as new obstacle information becomes available through external sensors. A conditional shortest path is a path of shortest Euclidean distance that is computed based on the avail...

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for ...

We consider the problem of planning shortest paths for a tethered robot with a finite length tether in a 2D environment with polygonal obstacles. We present an algorithm that runs in time O((kl +l)2rL4) and finds the shortest path or correctly determines that none exists that obeys the constraints;here n is the numberobstaclevertices,and kl is the numberloops in the initial configurationof the ...

Consider the Delaunay triangulation T of a set P of points in the plane. The spanning ratio of T , i.e. the maximum ratio between the length of the shortest path between this pair on the graph of the triangulation and their Euclidean distance. It has long been conjectured that the spanning ratio of T can be at most π/2. We show in this note that there exist point sets in convex position with a ...

We consider a constrained shortest path problem with the possibility to refill the resource at certain nodes. This problem is motivated by routing electric vehicles with a comparatively short cruising range due to the limited battery capacity. Thus, for longer distances the battery has to be recharged on the way. Furthermore, electric vehicles can recuperate energy during downhill drive. We ext...

We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) problem by reducing the Bounded-Distance Decoding (BDD) problem to uSVP and attempting to solve such instances using the ‘embedding’ approach. We experimentally derive a model for the success of the appr...