## 2 Related Works  
There are several approaches in the literature regarding the analysis of geographic trajectories. In fact, this is today an important research topic due to the increase in the volume of geographic information. [PERSON] and [PERSON] propose in [3] the analysis of real GPS trajectories collected from taxis operating in the city of Porto, moving buses in Dublin and Atlantic hurricanes from 1950 to 2004. In order to detect corridors, they discretize the trajectories using a grid and decompose the space in different sets of frequently observed locations. The Latent Dirichlet Allocation (LDA) model [4] is applied to the trajectory dataset to extract frequent traffic patterns. They apply a hierarchical clustering algorithm to the subtrajectories of each frequent set, following a bottom-up approach, using Dynamic Time Warping (DTW) [5] in order to measure the distance between two subtrajectories. Finally, another algorithm selects the set of corridors from the set of candidate corridors minimizing the Minimum Description Length (MDL) principle [6]. [PERSON] et al. [7] propose a system that suggests daily and local transport sharing opportunities for short-term trips, by analyzing the traces of urban mobility in Milan and Turin. Based on \"Call Detail Record\" (CDR) data, they propose algorithms to recognize similar paths that can be used to recommend shared rides. The data used for the experiments were provided by a telecom mobile operator and support a travel recommendation system for multiple users. General mobility routines are identified through an extension of the probabilistic generative LDA model, performed on the set of available trips, including among others, leisure mobility routines and commuting trips. Both referred works seek paths that are common to multiple users, organizing the movements made in time slots, but with different approaches. In both cases geographical distance is measured through the Haversine formula. [PERSON] et al. [8] consider the problem of detecting commuting patterns and propose new algorithms that cluster subpaths of given trajectories. The idea is to select a reference trajectory and then find all subtrajectories that are close to this one by using the Frechet distance. They consider the optimization problem of finding the longest cluster of a fixed size and the largest cluster of a fixed length. The Frechet distance is a distance measure for continuous shapes, such as curves and surfaces, and it is defined using reparameterisations of the shapes. Since it takes the continuity of the shapes under consideration, it is generally considered to be the most appropriate distance measure for curves. [PERSON] et al. propose in [9] a method to identify movement patterns of sets of trajectories and analyze simulated trajectories in a region of Itaim Quarter in Santa Catarina, Brazil. They consider the frequency distribution of points for identifying a set of frequent regions. The framework consists of two phases: a partitioning phase, in which the trajectories are segmented using the Minimum Description Length principle and a clustering phase, that considers the density to group similar segments in a cluster using the Frechet distance as a measure of similarity between curves. [PERSON] et al. [10] describe a new algorithm to compute Discrete Frechet Distance (DDF) which aims to lower computation time and improved precision. It includes three different improvements: the first one is the Douglas and Peucker filtering process. Indeed, for GPS trajectories, the number of positions can be dramatically reduced. The second one is a pruning process. Only a small part of the two matrices required to compute the discrete Frechet distance are computed. The last one is an improvement of the accuracy of the DDF. The proposed method is more complex than the regular discrete Frechet distance, but CPU time is reduced. In terms of accuracy, a balance between CPU time and precision is required.