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Abstract: Uncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths. With help from the operational law of uncertainty theory, this paper gives the uncertainty distribution of the shortest path length. Also, it investigates solutions to the -shortest path and the most shortest path in an uncertain network. It points out that there exists an equivalence relation between the -shortest path in an uncertain network and the shortest path in a corresponding deterministic network, which leads to an effective algorithm to find the -shortest path and the most shortest path. Roughly speaking, this algorithm can be broken down into two parts: constructing a deterministic network and then invoking the Dijkstra algorithm. [Copyright &y& Elsevier]

Abstract: Shortest path finding has a variety of applications in transportation and communication.In this paper, we study a well-known self-stabilizing algorithm for the shortest path problem for the distributed systems. The previous works on this topic had two assumptions that can be relaxed in this paper. First, in the previous works, the systems were assumed to be integral-weighted, whereas in this paper, the systems are real-weighted. Second, and more importantly, the previous works have shown that the algorithm is self-stabilizing under the more restricted central demon model, whereas in this paper, we give a rigorous proof showing that the algorithm is actually self-stabilizing under the more general distributed demon model. The work in this paper is of significance because in the existing literature on self-stabilizing systems, most of the papers regarding the distributed demon are for the ring networks only; there are very few papers that discuss the self-stabilizing algorithms for the general distributed systems assuming the distributed demon model. [Copyright &y& Elsevier]