||This article may be too technical for most readers to understand. (November 2009)|
|Graph and tree
IDA* is a variant of iterative deepening depth-first search that borrows the idea to use a heuristic function to evaluate the remaining cost to get to the goal from the A* search algorithm. Since it is based on iterative deepening depth-first search, its memory usage is lower than in A*, but unlike ordinary iterative deepening depth-first search, it concentrates on exploring the most promising nodes and thus doesn't go to the same depth everywhere in the search tree. Unlike A*, IDA* doesn't utilize dynamic programming and therefore often ends up exploring the same nodes many times.
While the standard iterative deepening depth-first search uses search depth as the cutoff for each iteration, the IDA* uses the more informative where is the cost to travel from the root to node and is the heuristic estimate of the cost to travel from to the solution.
node current node g the cost to reach current node f estimated cost of the cheapest path (root..node..goal) h(node) estimated cost of the cheapest path (node..goal) cost(node, succ) path cost function is_goal(node) goal test successors(node) node expanding function procedure ida_star(root, cost(), is_goal(), h()) bound := h(root) loop t := search(root, 0, bound) if t = FOUND then return FOUND if t = ∞ then return NOT_FOUND bound := t end loop end procedure function search(node, g, bound) f := g + h(node) if f > bound then return f if is_goal(node) then return FOUND min := ∞ for succ in successors(node) do t := search(succ, g + cost(node, succ), bound) if t = FOUND then return FOUND if t < min then min := t end for return min end function
Comparison to other algorithms
The A* search is one of the best general-purpose graph search algorithms when there's a way to estimate the distance to the goal. IDA* is slightly slower than A* (it explores the same nodes multiple times because it doesn't remember prior work) but is beneficial when the problem is memory constrained. A* search keeps a large queue of unexplored nodes that can quickly fill up memory. Because IDA* does not remember any node except the ones on the current path it has an extremely small memory profile.
IDA* requires an amount of memory that is linear in the length of the solution that it constructs. Its time complexity is analyzed by Korf et al. under the assumption that the heuristic cost estimate h is consistent, meaning that for all nodes n and all neighbors n' of n; they conclude that compared to a brute-force tree search over an exponential-sized problem, IDA* achieves a smaller search depth (by a constant factor), but not a smaller branching factor.
- Korf, Richard (1985). "Depth-first Iterative-Deepening: An Optimal Admissible Tree Search". Artificial Intelligence 27: 97–109. doi:10.1016/0004-3702(85)90084-0.
- Bonet, Blai; Geffner, Héctor C. (2001). "Planning as heuristic search". Artificial Intelligence 129: 5. doi:10.1016/S0004-3702(01)00108-4.
- Korf, Richard E.; Reid, Michael; Edelkamp, Stefan (2001). "Time complexity of iterative-deepening-A∗". Artificial Intelligence 129: 199. doi:10.1016/S0004-3702(01)00094-7.