Searching for and Comparing Trees and Graphs

1
Searching for and ComparingTrees and Graphs

• Dennis Shasha, shasha_at_cs.nyu.edu
• Courant Institute, NYU
• Joint work with
• Kaizhong Zhang and Jason Wang

2
Philosophy

• Trees and graphs represent data in many domains
  in linguistics, chemistry, and even maybe the
  web.
• Question why cant I search for trees or graphs
  at the speed of keyword searches?
• Why cant I compare trees (or graphs) as easily
  as I can compare strings?

3
Tree Searching

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

t
T
4
What does present mean?

• Preserving sibling order or not
• Preserving ancestor order
• Preserving distance
• Mismatches

5
Sibling Order

• Order of children of a node

A
A
?
B
B
C
C
6
Ancestor Order

• Order between children and parent.

C
A
?
A
B
C
B
7
Ancestor Distance

• Can children become grandchildren

A
A
?
X
B
B
C
C
8
Mismatches

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

A
A
how far?
C
B
X
C
9
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.

10
TreeSearch Query Language

• Query language is simply a tree decorated with
  single length dont cares (?) and variable length
  dont cares ().

A
0, on each side
?
1

C
D
B
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Exact Match

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

X
A
A
Y
Q
X
?

W
B

Z
D
C
D
U
B
C
12
Inexact Match

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

X
A
A
Y
Q
X
?
Differ by 1
W

B
Z
E
C
D
U
B
C
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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.

14
Treesearch Review

• Ancestor order matters.
• Sibling order doesnt.
• Dont 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

15
Screenshots of TreeSearch on TreeBASE
16
Query Screen
17
Query Tree Format
18
Search Results
19
Query Tree
20
One of the Result Trees
21
Related Work

• S. Amer-Yahia, S. Cho, L.V.S. Lakshmanan, and D.
  Srivastava. Minimization of tree pattern queries.
  SIGMOD, 2001.
• Z. Chen, H. V. Jagadish, F. Korn, N. Koudas, S.
  Muthukrishnan, R. T. Ng, and D. Srivastava.
  Counting twig matches in a tree. ICDE, 2001.
• J. Cracraft and M. Donoghue. Assembling the tree
  of life Research needs in phylogenetics and
  phyloinformatics. NSF Workshop Report, Yale
  University, 2000.

22
Tree Edit

• Order of children matters

A
A
A-A del(B) ins(B)
B
B
C
C
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Tree Edit in General

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

A
A
A-A del(X) ins(B)
B
X
C
C
C
C
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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.

25
Related Work

• IBM XML Diff and Merge Tool. http//www.alphaworks
  .ibm.com/aw.nsf/textResearchers/CB2EF938D7532F3388
  25671B0068244F
• K. Zhang and D. Shasha. Editing distance between
  trees. SIAM J. Comp., 1989.
• K. Zhang, D. Shasha and J. T. L. Wang.
  Approximate tree matching in the presence of
  variable length don't cares. Journal of
  Algorithms, 1994.

26
Graph Edit

• Thesis work of Rosalba Giugno.
• Find a small graph (with and ?) in a big graph.
• Doesnt work fast if query graph is big because
  graph subisomorphism is exponential.

27
Example of GraphGrep

• Query graph has nodes and dont cares

A
C
D

B
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Related Work

• P. Buneman, M. F. Fernandez, and D. Suciu. UnQL
  a query language and algebra for semistructured
  data based on structural recursion. VLDB Journal,
  2000.
• A. O. Mendelzon and P. T. Wood. Finding regular
  simple paths in graph databases. VLDB, 1989. 
• Daylight Chemical Information Systems. http//
  www.daylight.com/.
• Protein Structure Search. http//sss.berkeley.edu/
  
• Web Structure Search. http//www.almaden.ibm.com/c
  s/k53/clever.html

29
Summary of Tools

• Why cant 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.

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URLs for Tools

• http//www.cs.nyu.edu/shasha/papers/graphgrep
• http//cs.nyu.edu/cs/faculty/shasha/papers/treesea
  rch.html
• http//web.njit.edu/wangj/sigmod.html