The paper presents a new algorithm to determine the shortest, non-crossing, rectilinear paths in a twodimensional grid graph. The shortest paths are determined in a manner ensuring that they do not cross each other and bypass any obstacles present. Such shortest paths are applied in robotic chip design, suburban railway track layouts, routing traffic in wireless sensor networks, printed circuit board design routing, etc. When more than one equal length noncrossing path is present between the source and the destination, the proposed algorithm selects the path which has the least number of corners (bends) along the path. This feature makes the path more suitable for moving objects, such as unmanned vehicles. In the author’s scheme presented herein, the grid points are the vertices of the graph and the lines joining the grid points are the edges of the graph. The obstacles are represented by their boundary grid points. Once the graph is ready, an adjacency matrix is generated and the Floyd-Warshall all-pairs shortest path algorithm is used iteratively to identify the non-crossing shortest paths. To get the minimum number of bends in a path, we make a modification to the Floyd-Warshall algorithm, which is constitutes the main contribution of the author presented herein.
Minimum Number of Bends of Paths of Trees in a Grid Embedding
