Guided Forest Edit Distance: Better Structure Comparisons by Using Domain-knowledge Z.S. Peng H.F. Ting

The Forest Edit Distance

Edit distance of two ordered, labeled forests Edit operations between E and F  Relabling node i in E by the label of node j in F E F a h fm a me z v uy

Edit distance of two ordered, labeled forests Edit operations between E and F  Relabling node i in E by the label of node j in F  Relabel (3,5) E F a h fm a me z v uy  y

Edit distance of two ordered, labeled forests Edit operations between E and F  Relabling node i in E by the label of node j in F  Cost of the operation:  (3,5) E F a h fm a me z v uy  p

Edit distance of two ordered, labeled forests Edit operations between E and F  Delete node i from E E F a h fm a me z v uy

Edit distance of two ordered, labeled forests Edit operations between E and F  Delete node i from E  Delete (2,-) E F a h fm a me z v uy

Edit distance of two ordered, labeled forests Edit operations between E and F  Delete node i from E  Delete (2,-) E F a h m a me z v uy

Edit distance of two ordered, labeled forests Edit operations between E and F  Delete node i from E  Cost of the operation:  (2,-) E F a h m a me z v uy

Edit distance of two ordered, labelled forests Edit operations between E and F  Delete node j from F  The cost of operation:  (-,j) E F a h fm a me z v uy

Edit distance of two ordered, labelled forests The edit distance  (E,F) between E and F is the minimum cost of edit operations that transform E to E' and F to F' such that E' = F' E F a h fm a me z v uy a h fm a me z v uy

Edit distance of two ordered, labelled forests The edit distance  (E,F) between E and F is the minimum cost of edit operations that transform E to E' and F to F' such that E' = F' E F a h fm a me z v uy a h fm a me z v uy  e

Edit distance of two ordered, labelled forests The Guided edit distance  (E,F,G) between E and F with respect to a third forest G is the minimum cost of edit operations that transform E to E' and F to F' such that E' = F' include G as a subforest E F a h fm a me z v uy a m a mee 3 12 a me G

Application 1: RNA comparisons Cherry small circular viroid-Like RNA GI: between base 287 and base 337. T he Hammerhead motif of the RNA is printed in bold.

Application 2: Comparing XML documents XML documents with same Document Type Descriptor should be aligned with this DTD to get more accurate results

The algorithms  (E,F)  Tai 1979:  Zhang and Shasha 1989: where  Klein 1998:  (E,F,G) :  This paper:

Special Cases a a c c b a c c a c c f f

a a c c b a c c a c c f f Longest Constraint Common Subsequence Constrained Sequence Alignment

The algorithms Constrained Longest Common Subsequent  Tsai 2003: Constrained Sequence Alignment  Chin et al. : This paper: where Since G has one leaf, the time becomes

Our algorithm for computing  (E,F,G) Dynamic Programming

The sub-problems Post-order numbering (naming) of the nodes

The sub-problems : A "consecutive" sub-forest

The sub-problems : A "consecutive" sub-forest

The sub-problems E FG

The sub-problems E FG

is equal to the minimum of the followings:

E FG 

E FG 

E FG 

E FG

E FG

E FG

E FG

E FG

E FG

E FG

The order for solving the sub-problems for i=1 to |E| for j=1 to |F| for h=1 to |G| for k=1 to (|G|-h+1) if k is a leaf then find

The time complexity

Sparsify the dynamic program using a clever trick of Zhang and Shasha

key-root: if it is the root, or has a left-slibling E FG 2 1

E FG 2 1 No. of key-roots ≤ no. of leaves

To compute  (E,F,G)=  (E|| 1..|E|,F|| 1..|F|,G|| 1..|G| ) for i=1 to |E| for j=1 to |F| for h=1 to |G| for k=1 to (|G|-h+1) if k is a leaf find

To compute  (E,F,G)=  (E|| 1..|E|,F|| 1..|F|,G|| 1..|G| ) for i=1 to |E| for j=1 to |F| for h=1 to |G| for k=1 to (|G|-h+1) if k is a leaf and i and j are key-roots find

The new running time

Thank you