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Rooted trees (part 2) Lemma If there is O(n) algorithm for rooted trees isomorphism there is O(n) algorithm for ordinary trees isomorphism. Proof. 1 Let A to be O(n) algorithm for rooted trees. 2 Let T 1 and T 2 to be ordinary trees. 3 Lets find centers of this trees. There are three possibilities: 1 each tree has only one center (c 1 and c 2 respectively) return A(T 1 , c 1 , T 2 , c 2 ) 5 / 22
Rooted trees (part 2) Lemma If there is O(n) algorithm for rooted trees isomorphism there is O(n) algorithm for ordinary trees isomorphism. Proof. 1 Let A to be O(n) algorithm for rooted trees. 2 Let T 1 and T 2 to be ordinary trees. 3 Lets find centers of this trees. There are three possibilities: 1 each tree has only one center (c 1 and c 2 respectively) return A(T 1 , c 1 , T 2 , c 2 ) 2 each tree has exactly two centers (c 1 , c ′ 1 and c 2, c ′ 2 respectively) return A(T 1 , c 1 , T 2 , c 2 ) or A(T 1 , c ′ 1 , T 2, c 2 ) 5 / 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 15: 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 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
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AHU algorithm improvement Observati
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AHU algorithm example Example A a B
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AHU algorithm example Example A 1 2
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AHU algorithm example Example A 1 a
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Resume Resume • We have three uns
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