Conventionally the problem of the best path in a network refers to the shortest path problem.
However, for the vast majority of networks present nowadays this solution has some limitations which directly affect their proper functioning, as well as an inefficient use of their potentialities.
Problems at the level of large networks where graphs of high complexity are commonly present as well as the appearing of new services and their respective requirements, are intrinsically related to the inability of this solution. In order to overcome the needs present in these networks, a new approach to the problem of the best path must be explored. One solution that has aroused more interest in the scientific community considers the use of multiple paths
between two network nodes, where they can all now be considered as the best path between those nodes. Therefore, the routing will be discontinued only by minimizing one metric, where only one path between nodes is chosen, and shall be made by the selection of one of many paths, thereby allowing the use of a greater diversity of the present paths (obviously, if the network consents).
The establishment of multi-path routing in a given network has several advantages for its
operation. Its use may well improve the distribution of network traffic, improve recovery time to failure, or it can still offer a greater control of the network by its administrator. These factors still
have greater relevance when networks have large dimensions, as well as when their
constitution is of high complexity, such as the Internet, where multiple networks managed by different entities are interconnected. A large part of the growing need to use multipath protocols is associated to the routing made based on policies. Therefore, paths with different
characteristics can be considered with equal level of preference, and thus be part of the solution for the best way problem.
To perform multi-path routing using protocols based only on the destination address has some limitations but it is possible. Concepts of graph theory of algebraic structures can be used to describe how the routes are calculated and classified, enabling to model the routing problem.
This thesis studies and analyzes multi-path routing protocols from the known literature and derives a new algebraic condition which allows the correct operation of these protocols without any network restriction. It also develops a range of software tools that allows the planning and the respective verification/validation of new protocols models according to the study made
