The paper describes two relatively simple modifications of the well-known Floyd-Warshall algorithm for computing all-pairs shortest paths. A fundamental difference of both modifications in comparison to the Floyd-Warshall algorithm is that the relaxation is done in a smart way. We show that the expected-case time complexity of both algorithms is O(n 2 log 2 n) for the class of complete directed graphs on n vertices with arc weights selected independently at random from the uniform distribution on [0, 1]. Theoretically best known algorithms for this class of graphs are all based on Dijkstra's algorithm and obtain a better expected-case bound. However, by conducting an empirical evaluation we prove that our algorithms are at least competitive in practice with best know algorithms and, moreover, outperform most of them. The reason for the practical efficiency of the presented algorithms is the absence of use of priority queue. * A preliminary version of this work has been published in Shortest Path Solvers: From Software to Wetware, volume 32 of Emergence, Complexity and Computation (2018). The authors would like to thank the reviewer for excellent comments that substantially improved the quality of the paper.

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The manuscript proposes a new architecture for a Shallow Parsing and Shallow Transfer Rule-Based Machine Translation System. The newly proposed architecture omits the disambiguation module in the starting phases of the translation pipeline and stores all translation candidates generated by the ambiguous process in the morphological analysis phase. The architecture is based on multigraphs. We propose a simplified version of k-best shortest path algorithm for this special case of directed multigraph. The k-best set is ranked using a trigram language model. The empirical evaluation shows that the new architecture produces better translation quality results with constant delay in time.