Requests to Tsong-Li 1. Related work at end of each section 2. Screen dumps of treebase at end of treesearch section (you’ll see where) 3. Web addresses.

Requests to Tsong-Li

• 1. Related work at end of each section

• 2. Screen dumps of treebase at end of treesearch section (you’ll see where)

• 3. Web addresses at the very end.

Searching for and ComparingTrees and Graphs

Dennis Shasha, [email protected]

Courant Institute, NYU

Joint work with

Kaizhong Zhang and Jason Wang

Philosophy

• Trees and graphs represent data in many domains in linguistics, chemistry, and even maybe the web.

• Question: why can’t I search for trees or graphs at the speed of keyword searches?

• Why can’t I compare trees (or graphs) as easily as I can compare strings?

Tree Searching

• Given a small tree t is it present in a bigger tree T?

What does “present” mean?

• Preserving sibling order or not

• Preserving ancestor order

• Preserving distance

• Mismatches

Sibling Order

• Order of children of a node:

A

B C

A

C B

?=

Ancestor Order

• Order between children and parent.

A

B CA

C

B

?=

Ancestor Distance

• Can children become grandchildren:

A

B C

A

B X

?=

C

Mismatches

• Can there be relabellings, inserts, and deletes (Tolstoy problem):

A

B C

A

X C

howfar?

Bottom Line

• There is no one definition of mismatch or subtree (Tolstoy problem). You must choose the package that suits you.

• I will tell you about three.

TreeSearch Query Language

• Query language is simply a tree decorated with single length don’t cares (?) and variable length don’t cares (*).

A

*

B C

?

D

>= 0, oneach side

=1

Exact Match

• Query matches exactly if contained regardless of sibling order or other nodes

A

*

B C

?

D

=

X

Y A

W

Z

C

BX Q

DU

Inexact Match

• Inexact match if missing or differing node labels. Higher differences cost more.

A

*

B C

?

D

Differby 1

X

Y A

W

Z

C

BX Q

EU

Treesearch Conceptual Algorithm

• Take all paths in query tree.

• Find out where each path is in the data tree.

• So notion of distance is number of paths that differ. Higher nodes are more important.

• Implementation: suffix array. A few seconds on several thousand trees.

Treesearch Review

• Ancestor order matters.• Sibling order doesn’t.• Don’t cares: * and ?• Distance metric is based on numbers of path

differences.• Sister system built by Divesh and Sihem at

Bell Labs that allows terms to be “generalized”

Tsong-Li: screen dumps of treebase then related work

Tree Edit

• Order of children matters

A

B C

A’

C B

A->A’del(B)ins(B)

Tree Edit in General

• Operations are relabel A->A’, delete (X), insert (B).

A

X C

A’

C B

A->A’del(B)ins(B)

CC

Review of Tree Edit

• Generalizes string editing distance for trees, a dynamic programming algorithm.

• O(|T1| |T2| depth(T1) depth(T2))

• The basis for XMLdiff.

• Also has * and best removal of subtrees.

Tsong-Li: related work here

Graph Edit

• Thesis work of Rosalba Giugno.

• Find a small graph (with * and ?) in a big graph.

• Doesn’t work fast if query graph is big because graph subisomorphism is exponential.

Example of GraphGrep

• Query graph has nodes and don’t cares

A

B

* DC

Summary of Tools

• Why can’t tree and graph search be like keyword search?

• We are getting there and will provide software if you are interested.

• Current downloads of about 50.