On shortest path problems with "non-Markovian" link contribution to path lengths

In this paper we introduce a new class of shortest path problems, where the contribution of a link to the path length computation depends not only on the weight of that link but also on the weights of the links already traversed. This class of problems may be viewed as "non-Markovian". We consider a specific problem that belong to this class, which is encountered in the multimedia data transmission domain. We consider this problem under different conditions and develop algorithms. The shortest path problem in multimedia data transmission environment can be solved in O(n(2)) or O(n(3)) computational time.