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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.

In this work we propose the design principles of a stochastic graph-based model for the simulation of SARS-CoV-2 transmission. The proposed approach incorporates three sub-models, namely, the spatial model, the mobility model, and the propagation model, in order to develop a realistic environment for the study of the properties exhibited by the spread of SARS-CoV-2. The spatial model converts images of real cities taken from Google Maps into undirected weighted graphs that capture the spatial arrangement of the streets utilized next for the mobility of individuals. The mobility model implements a stochastic agent-based approach, developed in order to assign specific routes to individuals moving in the city, through the use of stochastic processes, utilizing the weights of the underlying graph to deploy shortest path algorithms. The propagation model implements both the epidemiological model and the physical substance of the transmission of an airborne virus considering the transmission parameters of SARS-CoV-2. Finally, we integrate these sub-models in order to derive an integrated framework for the study of the epidemic dynamics exhibited through the transmission of SARS-CoV-2., Comment: 10 Pages, 7 Figures, 2 Tables

In this work we propose the design principles behind the development of a smart application utilized by mobile devices in order to control the spread of SARS-CoV-2 coronavirus disease that caused the COVID-19 pandemic. Through the deployment of this application utilizing their Bluetooth enabled devices, individuals may keep track of their close contacts, and if nearby contacts using the same application are reported later as infected the proximate individual is informed in order to be quarantined for a short of time, preventing hence the spread of the virus. Through the latest year, there have been developed several applications in the Google Play Store that can be deployed by smart devices utilizing their Bluetooth connectivity for the nearby device tracking. However, in this work we propose an open architecture for the development of such applications, that also incorporates a more elaborated graph-theoretic and algorithmic background regarding the contact tracing. The proposed contact tracing algorithm, that can be embedded in the deployment of the application, provides a more immediate tracking of the contacts of an infected individuals, providing a wider extent in the tracing of the contacts, leading hence to a more immediate mitigation of the epidemic., Comment: 9 pages,4 figures

In the domain of software watermarking, we have proposed several graph theoretic watermarking codec systems for encoding watermark numbers $w$ as reducible permutation flow-graphs $F[\pi^*]$ through the use of self-inverting permutations $\pi^*$. Following up on our proposed methods, we theoretically study the oldest one, which we call W-RPG, in order to investigate and prove its resilience to edge-modification attacks on the flow-graphs $F[\pi^*]$. In particular, we characterize the integer $w\equiv\pi^*$ as strong or weak watermark through the structure of self-inverting permutations $\pi^*$ which encodes it. To this end, for any integer watermark $w \in R_n=[2^{n-1}, 2^n-1]$, where $n$ is the length of the binary representation $b(w)$ of $w$, we compute the minimum number of 01-modifications needed to be applied on $b(w)$ so that the resulting $b(w')$ represents the valid watermark number $w'$; note that a number $w'$ is called valid (or, true-incorrect watermark number) if $w'$ can be produced by the W-RPG codec system and, thus, it incorporates all the structural properties of $\pi^* \equiv w$., Comment: 17 pages, 1 figure

In this work we propose a graph-based model that, utilizing relations between groups of System-calls, distinguishes malicious from benign software samples and classifies the detected malicious samples to one of a set of known malware families. More precisely, given a System-call Dependency Graph (ScDG) that depicts the malware's behavior, we first transform it to a more abstract representation, utilizing the indexing of System-calls to a set of groups of similar functionality, constructing thus an abstract and mutation-tolerant graph that we call Group Relation Graph (GrG); then, we construct another graph representation, which we call Coverage Graph (CvG), that depicts the dominating relations between the nodes of a GrG graph. Based on the research so far in the field, we pointed out that behavior-based graph representations had not leveraged the aspect of the temporal evolution of the graph. Hence, the novelty of our work is that, preserving the initial representations of GrG and CvG graphs, we focus on augmenting the potentials of theses graphs by adding further features that enhance its abilities on detecting and further classifying to a known malware family an unknown malware sample. To that end, we construct periodical instances of the graph that represent its temporal evolution concerning its structural modifications, creating another graph representation that we call Temporal Graphs. In this paper, we present the theoretical background behind our approach, discuss the current technological status on malware detection and classification and demonstrate the overall architecture of our proposed detection and classification model alongside with its underlying main principles and its structural key-components., Comment: 23 pages, 15 figures, 1 table

Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper, we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number $w$ as a self-inverting permutation $\pi^*$, an algorithm for encoding the self-inverting permutation $\pi^*$ into a reducible permutation graph $F[\pi^*]$ whose structure resembles the structure of real program graphs, as well as decoding algorithms which extract the permutation $\pi^*$ from the reducible permutation graph $F[\pi^*]$ and the number $w$ from $\pi^*$. Both the encoding and the decoding process takes time and space linear in the length of the binary representation of $w$. The two main components of our proposed codec system, i.e., the self-inverting permutation $\pi^*$ and the reducible permutation graph $F[\pi^*]$, incorporate the binary representation of the watermark~$w$ in their structure and possess important structural properties, which make our system resilient to attacks; to this end, we experimentally evaluated our system under edge modification attacks on the graph $F[\pi^*]$ and the results show that we can detect such attacks with high probability., Comment: 27 pages, 6 figures. arXiv admin note: text overlap with arXiv:1110.1194

Software watermarking has received considerable attention and was adopted by the software development community as a technique to prevent or discourage software piracy and copyright infringement. A wide range of software watermarking techniques has been proposed among which the graph-based methods that encode watermarks as graph structures. Following up on our recently proposed methods for encoding watermark numbers $w$ as reducible permutation flow-graphs $F[\pi^*]$ through the use of self-inverting permutations $\pi^*$, in this paper, we extend the types of flow-graphs available for software watermarking by proposing two different reducible permutation flow-graphs $F_1[\pi^*]$ and $F_2[\pi^*]$ incorporating important properties which are derived from the bitonic subsequences composing the self-inverting permutation $\pi^*$. We show that a self-inverting permutation $\pi^*$ can be efficiently encoded into either $F_1[\pi^*]$ or $F_2[\pi^*]$ and also efficiently decoded from theses graph structures. The proposed flow-graphs $F_1[\pi^*]$ and $F_2[\pi^*]$ enrich the repository of graphs which can encode the same watermark number $w$ and, thus, enable us to embed multiple copies of the same watermark $w$ into an application program $P$. Moreover, the enrichment of that repository with new flow-graphs increases our ability to select a graph structure more similar to the structure of a given application program $P$ thereby enhancing the resilience of our codec system to attacks., Comment: 10 pages, 2 figures

We study the propagation of a malicious software in a network of mobile devices, which are moving in a specific city area, and establish time bounds for the activation of a counter-measure, i.e., an antivirus or a cleaner in order to prevent pandemic. More precisely, given an initial infected population (mobile devices), we establish upper bounds on the time needed for a counter-measure to take effect after infection (response-time), in order to prevent the rest susceptible devices to get infected. Thus, within a period of time, we guarantee that not all the susceptible devices in the city get infected and the infected ones get sanitized. In our work, we first propose a malware propagation model along with a device mobility model and then, utilizing these models, we develop a simulator that we use to study the spread of malware in such networks. Finally, we provide experimental results for the pandemic prevention taken by our simulator for various response-time intervals., Comment: 13 pages, 33 figures

This work provides to web users copyright protection of their Portable Document Format (PDF) documents by proposing efficient and easily implementable techniques for PDF watermarking; our techniques are based on the ideas of our recently proposed watermarking techniques for software, image, and audio, expanding thus the digital objects that can be efficiently watermarked through the use of self-inverting permutations. In particular, we present various representations of a self-inverting permutation $\pi^*$ namely 1D-representation, 2D-representation, and RPG-representation, and show that theses representations can be efficiently applied to PDF watermarking. Indeed, we first present an audio-based technique for marking a PDF document $T$ by exploiting the 1D-representation of a permutation $\pi^*$, and then, since pages of a PDF document $T$ are 2D objects, we present an image-based algorithm for encoding $\pi^*$ into $T$ by first mapping the elements of $\pi^*$ into a matrix $A^*$ and then using the information stored in $A^*$ to mark invisibly specific areas of PDF document $T$. Finally, we describe a graph-based watermarking algorithm for embedding a self-inverting permutation $\pi^*$ into the document structure of a PDF file $T$ by exploiting the RPG-representation of $\pi^*$ and the structure of a PDF document. We have evaluated the embedding and extracting algorithms by testing them on various and different in characteristics PDF documents., Comment: 17 pages, 6 figures. arXiv admin note: text overlap with arXiv:1003.1796 by other authors

In this paper we present an elaborated graph-based algorithmic technique for efficient malware detection. More precisely, we utilize the system-call dependency graphs (or, for short ScD graphs), obtained by capturing taint analysis traces and a set of various similarity metrics in order to detect whether an unknown test sample is a malicious or a benign one. For the sake of generalization, we decide to empower our model against strong mutations by applying our detection technique on a weighted directed graph resulting from ScD graph after grouping disjoint subsets of its vertices. Additionally, we have developed a similarity metric, which we call NP-similarity, that combines qualitative, quantitative, and relational characteristics that are spread among the members of known malware families to archives a clear distinction between graph-representations of malware and the ones of benign software. Finally, we evaluate our detection model and compare our results against the results achieved by a variety of techniques proving the potentials of our model., Comment: 21 pages, 4 figures

Software watermarking involves embedding a unique identifier or, equivalently, a watermark value within a software to prove owner's authenticity and thus to prevent or discourage copyright infringement. Towards the embedding process, several graph theoretic watermarking algorithmic techniques encode the watermark values as graph structures and embed them in application programs. Recently, we presented an efficient codec system for encoding a watermark number $w$ as a reducible permutation graph $F[\pi^*]$ through the use of self-inverting permutations $\pi^*$. In this paper, we propose a dynamic watermarking model, which we call WaterRPG, for embedding the watermark graph $F[\pi^*]$ into an application program $P$. The main idea behind the proposed watermarking model is a systematic use of appropriate calls of specific functions of the program $P$. More precisely, for a specific input $I_{key}$ of the program $P$, our model takes the dynamic call-graph $G(P, I_{key})$ of $P$ and the watermark graph $F[\pi^*]$, and produces the watermarked program $P^*$ having the following key property: its dynamic call-graph $G(P^*, I_{key})$ is isomorphic to the watermark graph $F[\pi^*]$. Within this idea the program $P^*$ is produced by only altering appropriate calls of specific functions of the input application program $P$. We have implemented our watermarking model WaterRPG in real application programs and evaluated its functionality under various and broadly used watermarking assessment criteria. The evaluation results show that our model efficiently watermarks Java application programs with respect to several watermarking metrics like data-rate, bytecode instructions overhead, resiliency, time and space efficiency. Moreover, the embedded watermarks withstand several software obfuscation and optimization attacks., Comment: 27 pages, 11 pages

In a software watermarking environment, several graph theoretic watermark methods use numbers as watermark values, where some of these methods encode the watermark numbers as graph structures. In this paper we extended the class of error correcting graphs by proposing an efficient and easily implemented codec system for encoding watermark numbers as reducible permutation flow-graphs. More precisely, we first present an efficient algorithm which encodes a watermark number $w$ as self-inverting permutation $\pi^*$ and, then, an algorithm which encodes the self-inverting permutation $\pi^*$ as a reducible permutation flow-graph $F[\pi^*]$ by exploiting domination relations on the elements of $\pi^*$ and using an efficient DAG representation of $\pi^*$. The whole encoding process takes O(n) time and space, where $n$ is the binary size of the number $w$ or, equivalently, the number of elements of the permutation $\pi^*$. We also propose efficient decoding algorithms which extract the number $w$ from the reducible permutation flow-graph $F[\pi^*]$ within the same time and space complexity. The two main components of our proposed codec system, i.e., the self-inverting permutation $\pi^*$ and the reducible permutation graph $F[\pi^*]$, incorporate important structural properties which make our system resilient to attacks.

For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all graphs of G. Our goal is to compute an efficient representation of J(G). In particular, we consider two versions of this problem. In the explicit version we wish to construct the smallest join-reachability graph for G. In the implicit version we wish to build an efficient data structure (in terms of space and query time) such that we can report fast the set of vertices that reach a query vertex in all graphs of G. This problem is related to the well-studied reachability problem and is motivated by emerging applications of graph-structured databases and graph algorithms. We consider the construction of join-reachability structures for two graphs and develop techniques that can be applied to both the explicit and the implicit problem. First we present optimal and near-optimal structures for paths and trees. Then, based on these results, we provide efficient structures for planar graphs and general directed graphs.

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology \cite{Civan}, and the framework through which it was studied, we introduce the linear coloring on graphs. We provide an upper bound for the chromatic number $\chi(G)$, for any graph $G$, and show that $G$ can be linearly colored in polynomial time by proposing a simple linear coloring algorithm. Based on these results, we define a new class of perfect graphs, which we call co-linear graphs, and study their complement graphs, namely linear graphs. The linear coloring of a graph $G$ is a vertex coloring such that two vertices can be assigned the same color, if their corresponding clique sets are associated by the set inclusion relation (a clique set of a vertex $u$ is the set of all maximal cliques containing $u$); the linear chromatic number $\mathcal{\lambda}(G)$ of $G$ is the least integer $k$ for which $G$ admits a linear coloring with $k$ colors. We show that linear graphs are those graphs $G$ for which the linear chromatic number achieves its theoretical lower bound in every induced subgraph of $G$. We prove inclusion relations between these two classes of graphs and other subclasses of chordal and co-chordal graphs, and also study the structure of the forbidden induced subgraphs of the class of linear graphs., Comment: 21 pages, 7 figures

We consider a variant of the path cover problem, namely, the $k$-fixed-endpoint path cover problem, or kPC for short, on interval graphs. Given a graph $G$ and a subset $\mathcal{T}$ of $k$ vertices of $V(G)$, a $k$-fixed-endpoint path cover of $G$ with respect to $\mathcal{T}$ is a set of vertex-disjoint paths $\mathcal{P}$ that covers the vertices of $G$ such that the $k$ vertices of $\mathcal{T}$ are all endpoints of the paths in $\mathcal{P}$. The kPC problem is to find a $k$-fixed-endpoint path cover of $G$ of minimum cardinality; note that, if $\mathcal{T}$ is empty the stated problem coincides with the classical path cover problem. In this paper, we study the 1-fixed-endpoint path cover problem on interval graphs, or 1PC for short, generalizing the 1HP problem which has been proved to be NP-complete even for small classes of graphs. Motivated by a work of Damaschke, where he left both 1HP and 2HP problems open for the class of interval graphs, we show that the 1PC problem can be solved in polynomial time on the class of interval graphs. The proposed algorithm is simple, runs in $O(n^2)$ time, requires linear space, and also enables us to solve the 1HP problem on interval graphs within the same time and space complexity.

In this paper we examine the classes of graphs whose $K_n$-complements are trees and quasi-threshold graphs and derive formulas for their number of spanning trees; for a subgraph $H$ of $K_n$, the $K_n$-complement of $H$ is the graph $K_n-H$ which is obtained from $K_n$ by removing the edges of $H$. Our proofs are based on the complement spanning-tree matrix theorem, which expresses the number of spanning trees of a graph as a function of the determinant of a matrix that can be easily constructed from the adjacency relation of the graph. Our results generalize previous results and extend the family of graphs of the form $K_n-H$ admitting formulas for the number of their spanning trees., Comment: 13 pages, 2 figures