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Lecture 6 Dynamic Programming

Lecture 6 Dynamic Programming. 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. /ˈ foʊniːm / ) each sound might represent one of k phonemes.

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Lecture 6 Dynamic Programming

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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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