Properties of monotone heuristics 1)All monotone heuristics are admissible 2)Monotone heuristic is admissible at all nodes (if h(G)=0) 3)If a node is expanded using a monotone heuristic, A* has found the optimal route to that node 4)Therefore, there is no need to consider a node if it is already found.
{"Image DocumentName": "Properties of monotone heuristics", "Image ImageDescription": "All monotone heuristics are admissible. Monotone heuristic is admissible at all nodes (if h(G)=0) If a node is expanded using a monotone heuristic, A  has found the optimal route to that node. Therefore, there is no need to consider a node if it is already found. If this is assumed, and the heuristic is monotone, the algorithm is still admissible. If the monotone assumption is not true, we risk a non optimal solution. However, most heuristics are monotone.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}