A Delaunay triangulation-based shortest path algorithm with O(n log n) time in the Euclidean plane

In the Euclidean and/or λ-geometry planes with obstacles, the shortest path problem is to find an optimal path between source and destination. There are three different approaches to solve this problem in the Euclidean plane; roadmaps, cell decomposition and potential field. In roadmaps approach, visibility graph is considered as one of the most widely used methods. In this paper, we present a novel method based on the concepts of Delaunay triangulation, improved Dijkstra algorithm and Fermat points to construct a reduced visibility graph which can obtain the near-shortest path in the Euclidean plane. In another word, the length of path obtained by our algorithm is the shortest among two other fastest algorithms with O(n log n) time complexity in the literature, where n is the number of obstacles.