Tree isomorphism

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Rooted trees (part 2) Lemma If there is O(n) algorithm for rooted trees isomorphism, then there is O(n) algorithm for ordinary trees isomorphism. Proof. 1 Let A to be O(n) algorithm for rooted trees. 2 Let T1 and T2 to be ordinary trees. 3 Lets find centers of this trees. There are three cases: 1 each tree has only one center (c1 and c2 respectively) return A(T1, c1, T2, c2) 5 / 22
Rooted trees (part 2) Lemma If there is O(n) algorithm for rooted trees isomorphism, then there is O(n) algorithm for ordinary trees isomorphism. Proof. 1 Let A to be O(n) algorithm for rooted trees. 2 Let T1 and T2 to be ordinary trees. 3 Lets find centers of this trees. There are three cases: 1 each tree has only one center (c1 and c2 respectively) return A(T1, c1, T2, c2) 2 each tree has exactly two centers (c1, c ′ 1 and c2, c ′ 2 respectively) return A(T1, c1, T2, c2) or A(T1, c ′ 1 , T2, c2) 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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Example A B C AHU algorithm example
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Example A B C AHU algorithm example
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Example A AHU algorithm example B 1
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Example AHU algorithm example A 1 2
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Example A AHU algorithm example 1 a
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Resume Resume ∙ We have made thre
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Tree isomorphism

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