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We present an optimal and efficient algorithm for finding a shortest path in an elastic optical network. The algorithm is an adaptation of the Dijkstra shortest path algorithm, where we take into account the spectrum continuity and…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…
We introduce and study a novel problem of computing a shortest path tree with a minimum number of non-terminals. It can be viewed as an (unweighted) Steiner Shortest Path Tree (SSPT) that spans a given set of terminal vertices by shortest…
We study the energy-optimal shortest path problem for electric vehicles (EVs) in large-scale road networks, where recuperated energy along downhill segments introduces negative energy costs. While traditional point-to-point pathfinding…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We consider three shortest path problems in directed graphs with random arc lengths. For the first and the second problems, a risk measure is involved. While the first problem consists in finding a path minimizing this risk measure, the…
Planning for Autonomous Unmanned Ground Vehicles (AUGV) is still a challenge, especially in difficult, off-road, critical situations. Automatic planning can be used to reach mission objectives, to perform navigation or maneuvers. Most of…
The phenomenon of self-organization has been of special interest to the neural network community for decades. In this paper, we study a variant of the Self-Organizing Map (SOM) that models the phenomenon of self-organization of the…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…
We study the problem of minimizing overall trip time for battery electric vehicles in road networks. As battery capacity is limited, stops at charging stations may be inevitable. Careful route planning is crucial, since charging stations…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…
In this paper, we consider the Weighted Region Problem. In the Weighted Region Problem, the length of a path is defined as the sum of the weights of the subpaths within each region, where the weight of a subpath is its Euclidean length…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
Routing, modulation and spectrum allocation in elastic optical networks is a problem aiming at increasing the capacity of the network. Many algorithms such as shortest path algorithm can be used as the routing section of this problem. The…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…