Graph-based algorithms for the efficient solution of a class of optimization problems

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and to the linear subcase. With numerical experiments, we show that the proposed algorithms outperform generic commercial solvers.Comment: 27 pages, 9 figures, 1 tabl

The Bounded Acceleration Shortest Path problem: complexity and solution algorithms

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a mobile vehicle and the arcs are associated to pre-assigned geometric paths that connect these positions. BASP consists in finding the minimum-time path between two nodes. Differently from SP, we require that the vehicle satisfy bounds on maximum and minimum acceleration and speed, that depend on the vehicle position on the currently traveled arc. We prove that BASP is NP-hard and define solution algorithm that achieves polynomial time-complexity under some additional hypotheses on problem data.Comment: 39 page

Intermittency and multifractional Brownian character of geomagnetic time series

Abstract. The Earth's magnetosphere exhibits a complex behavior in response to the solar wind conditions. This behavior, which is described in terms of mutifractional Brownian motions, could be the consequence of the occurrence of dynamical phase transitions. On the other hand, it has been shown that the dynamics of the geomagnetic signals is also characterized by intermittency at the smallest temporal scales. Here, we focus on the existence of a possible relationship in the geomagnetic time series between the multifractional Brownian motion character and the occurrence of intermittency. In detail, we investigate the multifractional nature of two long time series of the horizontal intensity of the Earth's magnetic field as measured at L'Aquila Geomagnetic Observatory during two years (2001 and 2008), which correspond to different conditions of solar activity. We propose a possible double origin of the intermittent character of the small-scale magnetic field fluctuations, which is related to both the multifractional nature of the geomagnetic field and the intermittent character of the disturbance level. Our results suggest a more complex nature of the geomagnetic response to solar wind changes than previously thought

A Dynamic Programming Approach for Road Traffic Estimation

We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group follows a different path. The flows of all user groups are modeled as a set of independent Poisson processes. Our focus is estimating the paths followed by each user group, and the means of the associated Poisson processes. We present a possible solution based on a Dynamic Programming algorithm. The method relies on the knowledge of high order cumulants. We discuss the theoretical properties of the introduced method. Finally, we present some numerical tests on well-known benchmark networks, using synthetic data

An algorithm with improved complexity for pebble motion/multi-agent path finding on trees

The pebble motion on trees (PMT) problem consists in finding a feasible sequence of moves that repositions a set of pebbles to assigned target vertices. This problem has been widely studied because, in many cases, the more general Multi-Agent path finding (MAPF) problem on graphs can be reduced to PMT. We propose a simple and easy to implement procedure, which finds solutions of length O(knc + n^2), where n is the number of nodes, $k$ is the number of pebbles, and c the maximum length of corridors in the tree. This complexity result is more detailed than the current best known result O(n^3), which is equal to our result in the worst case, but does not capture the dependency on c and k

ON THE EMERGENCE OF A 1/k SPECTRUM IN THE SUB-INERTIAL DOMAIN OF TURBULENT MEDIA

Several physical and astrophysical fluid and plasma systems displaying turbulent features show a 1/k (or 1/f) spectral domain at spatial (temporal) scales above the inertial range. Here, we investigate the formation of a 1/k spectral domain in fluid and MHD turbulence systems in the sub-inertial range (, where k0 is the injection scale) by means of shell-model simulations. The simulation results suggest that the 1/k domain emerges as a consequence of competing direct and inverse cascading processes, implying the formation and dissipation of large-scale gradients below the inertial domain. The relevance of our results for observations in space and astrophysical contexts is briefly discussed