Due to the process of network convergence, the variety of types of traffic transmitted over a single medium increases steeply. This phenomenon can be handled by the existing networking structure although the protocols that are used and, especially, the underlying routing protocols need to be improved. The problem of finding the shortest path on the Internet can no longer be easily defined as there is an increasing number of different characteristics to describe a point-to-point link. The definition of the shortest path may differ for different traffic types. Therefore, in the mathematical models used to solve the modern routing problems multiple criteria must be taken into account. One of the interesting classes of the optimization problem is the problem of finding the solution that is minimized against one of the criteria under certain constraints with regard to the others. In this paper, two algorithms solving this kind of problems are presented and compared with a new solution proposed by the authors.
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