algorithm - How to solve Subtree Isomorphism using maximum bipartite matching? -


how determine if given tree t contains subtree isomorphic tree s?

two trees called isomorphic if 1 of them can obtained other series of flips, i.e. swapping left , right children of number of nodes. number of nodes @ level can have children swapped. 2 empty trees isomorphic.

i've read @ few places bipartiate matching algorithms can used solve problem can't find non-paywalled sources details. there seems many research papers on problem, of them again behind paywall, i'm not interested in latest research algorithm problem. question how bipartiate matching applies problem?

ps: there seems confusion on internet meant "isomorphic". above definition found @ places places mentioned "isomorphic" means trees of same shape regardless of node values. if can clear confusion, had great too.

i'm going talk rooted subtree isomorphism; unrooted case can handled without regard efficiency trying roots.

the basic idea if have trees

               b    /|\          /|\   / | \        / | \  /  |  \      /  |  \ a1 ...    b1 ...  bn /\      /\   /\      /\

and want know whether a subtree of b in such way a maps b, i , j, compute recursively whether subtree rooted @ ai subtree of tree rooted @ bj in such way ai maps bj. (the base cases when a or b leaf.) now, it's not enough each subtree mappable, because if bj has particularly rich structure, several ais might subtrees, requirements of isomorphism won't let them share bj. maximum matching comes in: try match of ais bjs in such way subtrees can mapped.

to general rooted problem, try possible choices of b.


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