Tree isomorphism

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Contrary instance T1 a A b c B C d e f D E F g 1 G . n Candidate 3 (part 2) 1 . n T2 level degree spectrum (0, 0, 1, 0, . . .) (0, 1, 1, 0, . . .) (2, 0, 1, 0, . . .) (1, 1, 0, 0, . . .) . (1, 0, 0, 0, . . .) 12 / 22
Algorithm by Aho, Hopcroft and Ullman ∙ Determine tree <strong>isomorphism</strong> in time O(|V |). AHU algorithm ∙ Uses complete history of degree spectrum of the vertex descendants as a complete invariant. 13 / 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 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: Candidate 3 Conjecture Two trees ar
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

Tree isomorphism

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