Tree isomorphism

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Diameter and center Definition The diameter of tree is the length of the longest path. Definition A center is a vertex v such that the longest path from v to a leaf is minimal over all vertices in the tree. Algorithm 1: Choose a random root r. 2: Find a vertex v1 — the farthest form r. 3: Find a vertex v2 — the farthest form v1. 4: Diameter is a length of path from v1 to v2. 5: Centers are median elements of path from v1 to v2. It is O(n) algorithm. 6 / 22
The idea Let’s try to find complete invariant of rooted trees <strong>isomorphism</strong>. 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: Diameter and center Definition The
Page 25 and 26: The idea Let’s try to find comple
Page 27 and 28: 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:
Example A B C AHU algorithm example
Page 75 and 76:
Example A B C AHU algorithm example
Page 77 and 78:
Example A AHU algorithm example B 1
Page 79 and 80:
Example AHU algorithm example A 1 2
Page 81 and 82:
Example A AHU algorithm example 1 a
Page 83 and 84:
Resume Resume ∙ We have made thre
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Tree isomorphism

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