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Dynamic Programming Examples: Viterbi's Algorithm & Max Independent Set on Trees

Learn about Viterbi's Algorithm for voice recognition and finding maximum independent sets on trees using dynamic programming. Solve phoneme sequence scoring and node connectivity challenges efficiently!

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Dynamic Programming Examples: Viterbi's Algorithm & Max Independent Set on Trees

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  1. Lecture 6 Dynamic Programming

  2. Example 4 Viterbi’s Algorithm • Consider a simplified version of a voice recognition problem • Goal: Given n segments of sounds, output the phonemes (e.g. /ˈfoʊniːm/)each sound might represent one of k phonemes. • Input: For each sound segment, a list of scores for the k phonemes. For every pair of phonemes, a score for how likely one comes after the other • Goal: Find a sequence of phonemes that has the highest score.

  3. Example • n = 3, k = 2 • Input: • Optimal solution: 1 2 1Score = (5 + 3 + 4) + (5 + 4) = 21

  4. Example 5:Max Independent Set on Trees • Input: a tree • Independent Set: Set of nodes that are not connected by any edges • Goal: Find an independent set of maximum size.

  5. Max Independent Set on Trees • Input: a tree • Independent Set: Set of nodes that are not connected by any edges • Goal: Find an independent set of maximum size.

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