Convex Quadratic Programming Approach to the Maximum Matching Problem

The problem of determining a maximum matching or whether there exists a perfect matching, is very common in a large variety of applications and as been extensively studied in graph theory. In this paper we start to introduce a characterisation of a family of graphs for which its stability number is determined by convex quadratic programming. The main results connected with the recognition of this family of graphs are also introduced. It follows a necessary and sufficient condition which characterise a graph with a perfect matching and an algorithmic strategy, based on the determination of the stability number of line graphs, by convex quadratic programming, applied to the determination of a perfect matching. A numerical example for the recognition of graphs with a perfect matching is described. Finally, the above algorithmic strategy is extended to the determination of a maximum matching of an arbitrary graph and some related results are presented.

Mobility in vehicular networks with multiple access points to the infrastructure

Nowadays there is a huge evolution in the technological world and in the wireless networks. The electronic devices have more capabilities and resources over the years, which makes the users more and more demanding. The necessity of being connected to the global world leads to the arising of wireless access points in the cities to provide internet access to the people in order to keep the constant interaction with the world. Vehicular networks arise to support safety related applications and to improve the traffic flow in the roads; however, nowadays they are also used to provide entertainment to the users present in the vehicles. The best way to increase the utilization of the vehicular networks is to give to the users what they want: a constant connection to the internet. Despite of all the advances in the vehicular networks, there were several issues to be solved. The presence of dedicated infrastructure to vehicular networks is not wide yet, which leads to the need of using the available Wi-Fi hotspots and the cellular networks as access networks. In order to make all the management of the mobility process and to keep the user’s connection and session active, a mobility protocol is needed. Taking into account the huge number of access points present at the range of a vehicle for example in a city, it will be beneficial to take advantage of all available resources in order to improve all the vehicular network, either to the users and to the operators. The concept of multihoming allows to take advantage of all available resources with multiple simultaneous connections. This dissertation has as objectives the integration of a mobility protocol, the Network-Proxy Mobile IPv6 protocol, with a host-multihoming per packet solution in order to increase the performance of the network by using more resources simultaneously, the support of multi-hop communications, either in IPv6 or IPv4, the capability of providing internet access to the users of the network, and the integration of the developed protocol in the vehicular environment, with the WAVE, Wi-Fi and cellular technologies. The performed tests focused on the multihoming features implemented on this dissertation, and on the IPv4 network access for the normal users. The obtained results show that the multihoming addition to the mobility protocol improves the network performance and provides a better resource management. Also, the results show the correct operation of the developed protocol in a vehicular environment.

The Riemann-Hilbert method applied to the theory of orthogonal polynomials

Doutoramento em Matemática

DACA: architecture to implement dynamic access control mechanisms on business tier components

Access control is a software engineering challenge in database applications. Currently, there is no satisfactory solution to dynamically implement evolving fine-grained access control mechanisms (FGACM) on business tiers of relational database applications. To tackle this access control gap, we propose an architecture, herein referred to as Dynamic Access Control Architecture (DACA). DACA allows FGACM to be dynamically built and updated at runtime in accordance with the established fine-grained access control policies (FGACP). DACA explores and makes use of Call Level Interfaces (CLI) features to implement FGACM on business tiers. Among the features, we emphasize their performance and their multiple access modes to data residing on relational databases. The different access modes of CLI are wrapped by typed objects driven by FGACM, which are built and updated at runtime. Programmers prescind of traditional access modes of CLI and start using the ones dynamically implemented and updated. DACA comprises three main components: Policy Server (repository of metadata for FGACM), Dynamic Access Control Component (DACC) (business tier component responsible for implementing FGACM) and Policy Manager (broker between DACC and Policy Server). Unlike current approaches, DACA is not dependent on any particular access control model or on any access control policy, this way promoting its applicability to a wide range of different situations. In order to validate DACA, a solution based on Java, Java Database Connectivity (JDBC) and SQL Server was devised and implemented. Two evaluations were carried out. The first one evaluates DACA capability to implement and update FGACM dynamically, at runtime, and, the second one assesses DACA performance against a standard use of JDBC without any FGACM. The collected results show that DACA is an effective approach for implementing evolving FGACM on business tiers based on Call Level Interfaces, in this case JDBC.