Distances of centroid sets in a graph-based construction for information security applications

The aim of this paper is to prove that, for every balanced digraph, in every incidence semiring over a semifield, each centroid set J of the largest distance also has the largest weight, and the distance of J is equal to its weight. This result is surprising and unexpected, because examples show that distances of arbitrary centroid sets in incidence semirings may be strictly less than their weights. The investigation of the distances of centroid sets in incidence semirings of digraphs has been motivated by the information security applications of centroid sets.

First-priority relation graph-based malicious users detection in mobile social networks

Mobile social networks (MSNs) consist of many mobile users (individuals) with social characteristics, that provide a variety of data delivery services involving the social relationship among mobile individuals. Because mobile users move around based on their common interests and contact with each other more frequently if they have more social features in common in MSNs. In this paper, we first propose the first-priority relation graph, say FPRG, of MSNs. However, some users in MSNs may be malicious. Malicious users can break the data delivery through terminating the data delivery or tampering with the data. Therefore, malicious users will be detected in the process of looking for the data delivery routing to obtain efficient and reliable data delivery routing along the first-priority relation graph. Secondly, we propose one hamiltonian cycle decomposition of FPRG-based adaptive detection algorithm based on in MSNs under the PMC detection model (the system-level detection model).

Personalized recommendation on multi-layer context graph

Recommender systems have been successfully dealing with the problem of information overload. A considerable amount of research has been conducted on recommender systems, but most existing approaches only focus on user and item dimensions and neglect any additional contextual information, such as time and location. In this paper, we propose a Multi-Layer Context Graph (MLCG) model which incorporates a variety of contextual information into a recommendation process and models the interactions between users and items for better recommendation. Moreover, we provide a new ranking algorithm based on Personalized PageRank for recommendation in MLCG, which captures users' preferences and current situations. The experiments on two real-world datasets demonstrate the effectiveness of our approach.

Polyhedral results for the Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP)

In recent years, there has been studies on the cardinality constrained multi-cycle problems on directed graphs, some of which considered chains co-existing on the same digraph whilst others did not. These studies were inspired by the optimal matching of kidneys known as the Kidney Exchange Problem (KEP). In a KEP, a vertex on the digraph represents a donor-patient pair who are related, though the kidney of the donor is incompatible to the patient. When there are multiple such incompatible pairs in the kidney exchange pool, the kidney of the donor of one incompatible pair may in fact be compatible to the patient of another incompatible pair. If Donor A’s kidney is suitable for Patient B, and vice versa, then there will be arcs in both directions between Vertex A to Vertex B. Such exchanges form a 2-cycle. There may also be cycles involving 3 or more vertices. As all exchanges in a kidney exchange cycle must take place simultaneously, (otherwise a donor can drop out from the program once his/her partner has received a kidney from another donor), due to logistic and human resource reasons, only a limited number of kidney exchanges can occur simultaneously, hence the cardinality of these cycles are constrained. In recent years, kidney exchange programs around the world have altruistic donors in the pool. A sequence of exchanges that starts from an altruistic donor forms a chain instead of a cycle. We therefore have two underlying combinatorial optimization problems: Cardinality Constrained Multi-cycle Problem (CCMcP) and the Cardinality Constrained Cycles and Chains Problem (CCCCP). The objective of the KEP is either to maximize the number of kidney matches, or to maximize a certain weighted function of kidney matches. In a CCMcP, a vertex can be in at most one cycle whereas in a CCCCP, a vertex can be part of (but in no more than) a cycle or a chain. The cardinality of the cycles are constrained in all studies. The cardinality of the chains, however, are considered unconstrained in some studies, constrained but larger than that of cycles, or the same as that of cycles in others. Although the CCMcP has some similarities to the ATSP- and VRP-family of problems, there is a major difference: strong subtour elimination constraints are mostly invalid for the CCMcP, as we do allow smaller subtours as long as they do not exceed the size limit. The CCCCP has its distinctive feature that allows chains as well as cycles on the same directed graph. Hence, both the CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights. Most existing studies focused on solution methodologies, and as far as we aware, there is no polyhedral studies so far. In this paper, we will study the polyhedral structure of the natural arc-based integer programming models of the CCMcP and the CCCCP, both containing exponentially many constraints. We do so to pave the way for studying strong valid cuts we have found that can be applied in a Lagrangean relaxation-based branch-and-bound framework where at each node of the branch-and-bound tree, we may be able to obtain a relaxation that can be solved in polynomial time, with strong valid cuts dualized into the objective function and the dual multipliers optimised by subgradient optimisation.

VGraph: graph virtualization towards big data

Virtualization brought an immense commute in the modern technology especially in computer networks since last decade. The enormity of big data has led the massive graphs to be increased in size exponentially in recent years so that normal tools and algorithms are going weak to process it. Size diminution of the massive graphs is a big challenge in the current era and extraction of useful information from huge graphs is also problematic. In this paper, we presented a concept to design the virtual graph vGraph in the virtual plane above the original plane having original massive graph and proposed a novel cumulative similarity measure for vGraph. The use of vGraph is utile in lieu of massive graph in terms of space and time. Our proposed algorithm has two main parts. In the first part, virtual nodes are designed from the original nodes based on the calculation of cumulative similarity among them. In the second part, virtual edges are designed to link the virtual nodes based on the calculation of similarity measure among the original edges of the original massive graph. The algorithm is tested on synthetic and real-world datasets which shows the efficiency of our proposed algorithms.

Graph theory based QoE-driven cooperation stimulation for content dissemination in device-To-device communication

With multimedia dominating the digital contents, Device-To-Device (D2D) communication has been proposed as a promising data offloading solution in the big data area. As the quality of experience (QoE) is a major determining factor in the success of new multimedia applications, we propose a QoEdriven cooperative content dissemination (QeCS) scheme in this work. Specifically, all users predict the QoE of the potential connections characterized by the mean opinion score (MOS), and send the results to the content provider (CP). Then CP formulates a weighted directed graph according to the network topology and MOS of each potential connection. In order to stimulate cooperation among the users, the content dissemination mechanism is designed through seeking 1-factor of the weighted directed graph with the maximum weight thus achieving maximum total user MOS. Additionally, a debt mechanism is adopted to combat the cheat attacks. Furthermore, we extend the proposed QeCS scheme by considering a constrained condition to the optimization problem for fairness improvement. Extensive simulation results demonstrate that the proposed QeCS scheme achieves both efficiency and fairness especially in large scale and density networks.