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Simplified Memory Bounded A* Search

September 4, 2010 Leave a comment

The Simplified Memory-Bounded Algorithm (SMA*) is a variant of A* search which is memory-bounded.

  • Complete & optimal if enough memory is available to store shallowest solution path.
  • To enqueue new expand, dequeue the unpromising node with highest f-cost.
  • Retains ancestor node information about the quality of the best path in the forgotten sub tree.

Regenerate forgotten node if all other paths look worse.

Iterative Deepening A* Search

September 4, 2010 Leave a comment

Modification of A* search use f-cost limit as depth bound

  • Increase threshold as minimum of f(.) of previous cycle
  • Each iteration expands all nodes inside the contour for current f-cost
  • complete and optimal
  • Same order of node expansion
  • Storage Efficient – practical

IDA* do not remember history

Therefore cannot avoid repeated states

A* Search

September 4, 2010 Leave a comment
An example of A star (A*) algorithm in action ...

Image via Wikipedia

A* uses a best-first search and finds the least-cost path from a given initial node to one goal node (out of one or more possible goals).

It uses a distance-plus-cost heuristic function (usually denoted f(x)) to determine the order in which the search visits nodes in the tree. The distance-plus-cost heuristic is a sum of two functions:

  • The path-cost function, which is the cost from the starting node to the current node (usually denoted g(x))
  • In addition, an admissible “heuristic estimate” of the distance to the goal (usually denoted h(x)).

Best-First Search (Greedy Search)

September 4, 2010 2 comments

Best-first search is a search algorithm, which explores a graph by expanding the most promising node chosen according to a specified rule.

Judea Pearl described best-first search as estimating the promise of node n by a “heuristic evaluation function f(n) which, in general, may depend on the description of n, the description of the goal, the information gathered by the search up to that point, and most important, on any extra knowledge about the problem domain.”

Some authors have used “best-first search” to refer specifically to a search with a heuristic that attempts to predict how close the end of a path is to a solution, so that paths, which are judged closer to a solution, are extended first. This specific type of search is called greedy best-first search.

Efficient selection of the current best candidate for extension is typically implemented using a priority queue

Comparison of Search Techniques

September 4, 2010 Leave a comment

Criterion

BFS

UCS

DFS

DLS

IDS

BS

Time

b­d

b­d

Bm

Bl

b­d

b­d/2

Space

b­d

b­d

bm

bl

bd

b­d/2

Optimal?

Yes

Yes

No

No

Yes

Yes

Complete?

Yes

Yes

No

Yes,

If l>=d

Yes

Yes

Bidirectional search

September 4, 2010 Leave a comment

Bidirectional search is a graph search algorithm that finds a shortest path from an initial vertex to a goal vertex in a directed graph. It runs two simultaneous searches: one forward from the initial state and one backward from the goal, stopping when the two meet in the middle. The reason for this approach is that in many cases it is faster: for instance, in a simplified model of search problem complexity in which both searches expand a tree with branching factor b, and the distance from start to goal is d, each of the two searches has complexity O(bd/2) (in Big O notation), and the sum of these two search times is much less than the O(bd) complexity that would result from a single search from the beginning to the goal.

Iterative Deepening Search

September 4, 2010 1 comment

Iterative deepening depth-first search (IDDFS) is a state space search strategy in which a depth-limited search is run repeatedly, increasing the depth limit with each iteration until it reaches d, the depth of the shallowest goal state. On each iteration, IDDFS visits the nodes in the search tree in the same order as depth-first search, but the cumulative order in which nodes are first visited, assuming no pruning, is effectively breadth-first.

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