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The idea Let’s try to find complete invariant of rooted trees isomorphism. Definition Isomorphism invariant is a function f (T ) such that f (T 1 ) = f (T 2 ) for all pairs of isomorphic trees T 1 and T 2 . Definition Complete isomorphism invariant is a function f (T ) such that two trees T 1 and T 2 are isomorphic if and only if f (T 1 ) = f (T 2 ). So if we find complete isomorphism invariant we can obtain algorithm from it. 7 / 22
The idea Let’s try to find complete invariant of rooted trees isomorphism. Definition Isomorphism invariant is a function f (T ) such that f (T 1 ) = f (T 2 ) for all pairs of isomorphic trees T 1 and T 2 . Definition Complete isomorphism invariant is a function f (T ) such that two trees T 1 and T 2 are isomorphic if and only if f (T 1 ) = f (T 2 ). So if we find complete isomorphism invariant we can obtain algorithm from it. Note Starting from the next slide tree means rooted tree! 7 / 22
Page 1 and 2: Tree isomorphism Alexander Smal St.
Page 3 and 4: Graph isomorphism Definition Isomor
Page 5 and 6: Graph isomorphism Definition Isomor
Page 7 and 8: Rooted trees Definition Rooted tree
Page 13 and 14: Rooted trees (part 2) Lemma If ther
Page 19 and 20: Diameter and center Definition The
Page 21 and 22: Diameter and center Definition The
Page 23 and 24: The idea Let’s try to find comple
Page 25: The idea Let’s try to find comple
Page 29 and 30: Candidate 1 Observation The level n
Page 31 and 32: Candidate 1 Observation The level n
Page 33 and 34: Candidate 2 What’s wrong with can
Page 35 and 36: Candidate 2 (part 2) Observation Si
Page 37 and 38: Candidate 3 Conjecture Two trees ar
Page 39 and 40: Candidate 3 Conjecture Two trees ar
Page 41 and 42: Algorithm by Aho, Hopcroft and Ullm
Page 43 and 44: Algorithm by Aho, Hopcroft and Ullm
Page 45 and 46: Understanding AHU algorithm Knuth t
Page 57 and 58: Understanding AHU algorithm (part 3
Page 67 and 68: AHU algorithm improvement Observati
Page 73 and 74: AHU algorithm example Example A a B
Page 75 and 76: AHU algorithm example Example A a B
Page 77 and 78:
AHU algorithm example Example A a B
Page 79 and 80:
AHU algorithm example Example A 1 2
Page 81 and 82:
AHU algorithm example Example A 1 a
Page 83 and 84:
Resume Resume • We have three uns
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