An efficient label setting/correcting shortest path algorithm

We design a new label shortest path algorithm by applying the concept of a pseudo permanent label. This approach allows an algorithm to partition the set of nodes into two new sets: pseudo permanently labeled nodes and its complementary set. From this point of view, this new label method can be considered as label setting and is also a Dijkstra (1959) method. Moreover, during the execution of each iteration of the algorithm, at least one node becomes permanently labeled when some nodes which belong to the set of pseudo permanently labeled nodes are scanned. In the case of networks with non-negative length arcs is easy to prove that this node has the minimum distance label among the non-pseudo permanently labeled nodes. On the other hand which nodes belonging to the set of pseudo permanently labeled nodes that are permanently labeled nodes is unknown. Therefore, all distance labels are temporary and the algorithm becomes a label correcting method. Nevertheless, the proposed algorithm exhibits some nice features, such as: (1) the time bound for the running of the algorithm for a network with n nodes and m arcs is O(nm) (2) The theoretical number of scanned arcs in each iteration of the algorithm is less than the number of scanned arcs in each pass of the previous label correcting algorithms (3) The algorithm incorporates two new rules which allow easy detection of a negative cycle in the network. (4) The algorithm is quite simple and very easy to implement, and does not require sophisticated data structures. (5) The algorithm exhibits flexibility in the order in which the new pseudo permanently labeled nodes are scanned. The above features are possible through the application of the pseudo permanent label concept.