The level structure of a graph can be computed by a variant of breadth first search:
2.
Suggest a simplified version of this approach : they augment the graph to be maximal planar and construct a breadth first search tree as before.
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For solving those cases, I'd suggest maybe a breadth first search starting with the originally chosen point, and proceeding to neighbouring unsearched vertices?
4.
Because the tree contains each positive rational number exactly once, a breadth first search of the tree provides a method of listing all positive rationals that is closely related to Farey sequences.
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Jarvis and Shier describe a very similar algorithm using breadth first search in place of depth-first search; the advantage of depth-first search is that the strong connectivity analysis can be incorporated into the same search.
6.
Simply represent the game by an undirected graph, the nodes being distributions of disks and the edges being moves and use breadth first search to find one ( or all ) shortest path ( s ) moving a tower from one peg onto another one.
7.
In any graph, directed or undirected, there is a straightforward algorithm for finding a widest path once the weight of its minimum-weight edge is known : simply delete all smaller edges and search for any path among the remaining edges using breadth first search or depth first search.
8.
Another variation of tree search algorithms used is the Directed Breadth First Search ( DBS ), in which a child node to the current state is created for each available action, and visits each child ordered by highest average reward, until either the game ends or runs out of time.
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:: As for the " breadth first search " I was thinking of earlier ( which I guess your answer was mostly directed to ), I think I agree that it wouldn't work, but it was also not a polynomial time algorithm either .-Rainwarrior 16 : 17, 12 September 2006 ( UTC)
10.
The key new step involves using a breadth first search to partition the graph's vertices into levels according to their distances from some arbitrarily chosen root vertex, forming a graph from each level in which two vertices are adjacent if they share a common neighbor in the previous level, and searching for triangles in these graphs.
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