# Mobility, Citizens, Innovation and Technology in Digital and Smart Cities
## 2 The Search for an Optimized Urban Transportation Ecosystem
### Graph Modeling  
The topological/geometric nature of transportation systems and their dynamics motivates studies focused on graph theoretical models. [PERSON] and [PERSON] [21] revise that graph theory dates back to 1741, when mathematician [PERSON] had some insights about the \"The Seven Bridges of Konigsberg\", a problem that can be succinctly described as follows: find, if possible, a tour that traverses every edge of the graph exactly once and returns to the starting point.  
Modeling the novel class of transportation problems in a efficient manner, mostly dealing with huge amounts of information, increases the chance to achieve more efficient solutions, in accordance to what decision makers are looking for. For this purpose, we highlight the use of graph clustering techniques, as in [25; 26], since such tools can connect these new problems with works already addressed in the literature. For example, in [25], the problem of grouping parts to be produced and the machines that will process such parts into homogeneous cells is studied so that the number of faults (part-machine pairs that do not have relation) is minimized. The motivation for such a study comes from industrial planning and development, where optimizing transportation of parts between industrial parks is highly desired. In [26], efficient algorithms to solve the cluster editing problem (that consists of adding and/or removing the minimum number of edges in order to transform the input graph into a disjoint union of complete graphs or \"clusters\") have been described by the authors, motivated by applications that demand grouping data with high degree of similarity, while discarding spurious information. Such \"clustered solutions\" can be viewed as an attempt to cover large urban agglomerations by homogeneous, self-governing small cells that can work autonomously. A scatter search was designed by [PERSON] and [PERSON] [27] to solve a graph with stations and nodes, for moving jointly persons and goods in urban areas, in order to minimize energy consumption within the context of smart cities.  
Multi-modal transportation systems [28] are interesting examples for highlighting the actual complexity of urban transportation. This family of problems also can cover the locomotion for motor profile (reduced mobility). This kind of optimization can be dealt within the scope multi-objectiveoptimization [29; 30]. As an example, the Minimum Coloring Cut Problem (MCCP) is defined as follows: given a connected graph \(G\) with colored edges, find an edge cut \(E^{\prime}\) of \(G\) (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the edges in \(E^{\prime}\) is minimum. A potential application of the MCCP is in transportation planning systems, where nodes represent locations served by bus and edge colors represent bus companies. In this case, a solution of the MCCP gives the minimum number of companies that must stop working in order to create pairs of locations not reachable by bus from one another. Such application is more suitably modeled by allowing a multigraph as the input of the MCCP, since two locations can be connected by bus services offered by more than a single company.  
Furthermore, the so-called interruption graphs can be considered in post-disaster logistics, a problem of great importance for different events that may occur in urban centers. These approaches are suitable to assist with the human decision-making process, in particular, when huge disasters happen, such as the 2017 Irma hurricane. In order to promote better integration with citizens, it is also suggested to study and develop new techniques for processing huge graphs, using high-performance computing, in order to verify interaction between citizens, cities and social networks.