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Memoryless online routing (MOR) algorithms are suitable for the applications only using local information to find paths, and Delaunay triangulations (DTs) are the class of geometric graphs widely proposed as network topologies. Motivated by these two facts, this paper reports a variety of new MOR algorithms that work for Delaunay triangulations, thus greatly enriching the family of such algorithms. This paper also evaluates and compares these new algorithms with three existing MOR algorithms. The experimental results shed light on their performance in terms of both Euclidean and link metrics, and also reveal certain properties of Delaunay triangulations. Finally, this paper poses three open problems, with their importance explained.