File:Weighted A star with eps 5.gif

English: Illustration of weighted A* search with ${\displaystyle \epsilon =5.0}$, for faster, but sub-optimal path planning. The graph is created by uniform square discretization of a 2-dimensional planar region, placing a node in each discretized cell, and connecting each node with its 8 neighbors using bidirectional edges. Cost of edges are same as their Euclidean lengths. The gray shape represents an obstacle. The filled circles in red & green represent expanded nodes (nodes in closed set). The color indicate the g-score (red:lower g-score, green: higher g-score). The empty nodes with blue boundary are the ones in open set. The nodes of the graph are generated on the fly, and nodes falling inside the obstacle are discarded as inaccessible. The heuristic used by a node is 5 times its Euclidean distance to goal (note that Euclidean distance to goal is a consistent heuristic). The final path obtained is suboptimal when compared to the ones obtained using Dijkstra's algorithm or A* search algorithm, but the search is significantly faster. Created using YGSBPL graph-search library and OpenCV.