152 research outputs found
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, 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
- …