On revising arc weights from known shortest paths

Assume a positive directed weighted network. Suppose computed shortest paths for some pairs of nodes are found to be inconsistent with those known from other more reliable sources. This paper presents an algorithm to revise the original arc weights of the network so that the shortest paths based on the revised weights are consistent with those known from the more reliable sources. In comparison with another algorithm in the literature, the number of arc weights this algorithm needs to revise is smaller, and the computing time is likely to be shorter in some applications. In practice, the reliable sources can continuously provide additional information about shortest paths upon request. The algorithm is incorporated into a process which continuously refines the arc weights based on additional information until a prespecified standard is reached. The algorithms are mathematically simple. Numerical results are provided for illustration, and for comparison with the other algorithm in the literature.