This is a quick description of the Viterbi aka dynamic programming algorithm. Its reason for existence is that Wikipedia has become very poor on describing algorithms in a way that makes it useable for understanding them or anything else actually. It tends now to describe the very same algorithm under 50 different names and pages with few understandable by even people who fully understand the algorithm and the theory behind. Problem description: (that is what it can solve) assume we have a 2d table, or you could call it a graph or matrix if you prefer O O O O O O O O O O O O O O O O O O O O O O O O O O O O That table has edges connecting points from each column to the next column and each edge has a score like: (only some edge and scores shown to keep it readable) O--5--O-----O-----O-----O-----O 2 / 7 / \ / \ / \ / \ / \ / \ / \ / \ / O7-/--O--/--O--/--O--/--O--/--O \/ \/ 1/ \/ \/ \/ \/ \/ \/ \/ /\ /\ 2\ /\ /\ /\ /\ /\ /\ /\ O3-/--O--/--O--/--O--/--O--/--O / \ / \ / \ / \ / \ 1 \ 9 \ / \ / \ / \ O--2--O--1--O--5--O--3--O--8--O Our goal is to find a path from left to right through it which minimizes the sum of the score of all edges. (and of course left/right is just a convention here it could be top down too) Similarly the minimum could be the maximum by just flipping the sign, Example of a path with scores: O O O O O O O >---O. O O .O-2-O O O 5. .7 . O O-1-O O O 8 O O . O O O O O O-1-O---> (sum here is 24) The Viterbi algorithm now solves this simply column by column For the previous column each point has a best path and a associated score: O-----5 O \ \ O \ 1 O \/ /\ O / 2 O / / O-----2 O To move one column forward we just need to find the best path and associated scores for the next column here are some edges we could choose from: O-----5--3--O \ \8 \ \ O \ 1--9--O \/ \3 /\ \ O / 2--1--O / \2 / \ O-----2--4--O Finding the new best paths and scores for each point of our new column is trivial given we know the previous column best paths and scores: O-----0-----8 \ \ O \ 0----10 \/ /\ O / 0-----3 / \ / \ O 0 4 the Viterbi algorithm continues exactly like this column for column until the end and then just picks the path with the best score (above that would be the one with score 3) Author: Michael Niedermayer Copyright LGPL