SMA* explained

SMA* or Simplified Memory Bounded A* is a shortest path algorithm based on the A* algorithm. The main advantage of SMA* is that it uses a bounded memory, while the A* algorithm might need exponential memory. All other characteristics of SMA* are inherited from A*.

Properties

SMA* has the following properties

• It works with a heuristic, just as A*
• It is complete if the allowed memory is high enough to store the shallowest solution
• It is optimal if the allowed memory is high enough to store the shallowest optimal solution, otherwise it will return the best solution that fits in the allowed memory
• It avoids repeated states as long as the memory bound allows it
• It will use all memory available
• Enlarging the memory bound of the algorithm will only speed up the calculation
• When enough memory is available to contain the entire search tree, then calculation has an optimal speed

Implementation

The implementation of Simple memory bounded A* is very similar to that of A*; the only difference is that nodes with the highest f-cost are pruned from the queue when there isn't any space left. Because those nodes are deleted, simple memory bounded A* has to remember the f-cost of the best forgotten child of the parent node. When it seems that all explored paths are worse than such a forgotten path, the path is regenerated.^[1]

Pseudo code:function simple memory bounded A*-star(problem): path queue: set of nodes, ordered by f-cost;begin queue.insert(problem.root-node);

while True do begin if queue.empty then return failure; //there is no solution that fits in the given memory node := queue.begin; // min-f-cost-node if problem.is-goal(node) then return success; s := next-successor(node) if !problem.is-goal(s) && depth(s)

max_depth then f(s) := inf; // there is no memory left to go past s, so the entire path is useless else f(s) := max(f(node), g(s) + h(s)); // f-value of the successor is the maximum of // f-value of the parent and // heuristic of the successor + path length to the successor end if if no more successors then update f-cost of node and those of its ancestors if needed if node.successors ⊆ queue then queue.remove(node); // all children have already been added to the queue via a shorter way if memory is full then begin bad Node := shallowest node with highest f-cost; for parent in bad Node.parents do begin parent.successors.remove(bad Node); if needed then queue.insert(parent); end for end if

queue.insert(s); end whileend

Notes and References

1. Russell . S. . 1992 . 10.1.1.105.7839 . Efficient memory-bounded search methods . Proceedings of the 10th European Conference on Artificial intelligence . Vienna, Austria . B. . Neumann . John Wiley & Sons, New York, NY . 1–5 .