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In this work we propose the design principles of an integrated distributed system for the augment of the transportation for people with disabilities inside the road network of a city area utilizing the IT technologies. We propose the basis of our system upon the utilization of a distributed sensor network that will be incorporated by a real-time integrated feedback system. The main components of the proposed architecture include the Inaccessible City Point System, the Live Data Analysis and Response System, and the Obstruction Detection and Prevention System. The incorporation of these subsystems will provide real-time feedback assisting the transportation of individuals with mobility problems informing them on real-time about blocked ramps across the path defined to their destination, being also responsible for the information of the authorities about incidents regarding the collision of accessibility in place where the sensors detect an inaccessible point. The proposed design allows the addition of further extensions regarding the assistance of individuals with mobility problems providing a basis for its further implementation and improvement. In this work we provide the fundamental parts regarding the interconnection of the proposed architecture's components as also its potential deployment regarding the proposed architecture and its application in the area of a city., Comment: 7 pages, 6 figures

Consider a graph $G$ which belongs to a graph class ${\cal C}$. We are interested in connecting a node $w \not\in V(G)$ to $G$ by a single edge $u w$ where $u \in V(G)$; we call such an edge a \emph{tail}. As the graph resulting from $G$ after the addition of the tail, denoted $G+uw$, need not belong to the class ${\cal C}$, we want to compute a minimum ${\cal C}$-completion of $G+w$, i.e., the minimum number of non-edges (excluding the tail $u w$) to be added to $G+uw$ so that the resulting graph belongs to ${\cal C}$. In this paper, we study this problem for the classes of split, quasi-threshold, threshold, and $P_4$-sparse graphs and we present linear-time algorithms by exploiting the structure of split graphs and the tree representation of quasi-threshold, threshold, and $P_4$-sparse graphs.

The minimum completion (fill-in) problem is defined as follows: Given a graph family $\mathcal{F}$ (more generally, a property $\Pi$) and a graph $G$, the completion problem asks for the minimum number of non-edges needed to be added to $G$ so that the resulting graph belongs to the graph family $\mathcal{F}$ (or has property $\Pi$). This problem is NP-complete for many subclasses of perfect graphs and polynomial solutions are available only for minimal completion sets. We study the minimum completion problem of a $P_4$-sparse graph $G$ with an added edge. For any optimal solution of the problem, we prove that there is an optimal solution whose form is of one of a small number of possibilities. This along with the solution of the problem when the added edge connects two non-adjacent vertices of a spider or connects two vertices in different connected components of the graph enables us to present a polynomial-time algorithm for the problem.