The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: Dialing for Documents
``Graph problem? What graph problem? Where is there even a graph?''
``Think of a sentence as a list of phone tokens, each representing a word in the sentence. For each phone
token, we have a list of words from the dictionary that match it. How can we choose which one is right?
Each possible sentence interpretation can be thought of as a path in a graph. The vertices of this graph
will be the complete set of possible word choices. There will be an edge from a possible choice for the
ith word to each possible choice for the (i+1)st word. The cheapest path across this graph is the right
interpretation of the sentence.''
Figure: The minimum-cost path through the graph defines the best interpretation for a sentence
``But all the paths look the same. They have the same number of edges. Wait. Now I see! To make the
paths different, we have to weight the edges.''
``Exactly! The cost of an edge will reflect how likely it is that we will want to travel through the given
pair of words. Maybe we can count how often that pair of words occurred together in previous texts. Or
we can weight by what part of speech each word is. Maybe nouns don't like to be next to nouns as much
as they like being next to verbs.''
``It will be hard to keep track of word-pair statistics, since there are so many of them. But we certainly
know the frequency of each word. How can we factor that into things?''
``We can pay a cost for walking through a particular vertex that depends upon the frequency of the word.
Our best sentence will be given by the shortest path across the graph.''
``But how do we figure out the relative weights of these factors?''
``Well, try what seems natural to you and then we can experiment with it.''
Harald incorported this shortest-path algorithm. With proper grammatical and statistical constraints, the
system performed great, as reported in [RS96]. Look at the Gettysburg Address now, with all the
reconstruction errors highlighted:
FOURSCORE AND SEVEN YEARS AGO OUR FATHERS BROUGHT FORTH ON THIS
file:///E|/BOOK/BOOK2/NODE80.HTM (4 of 6) [19/1/2003 1:29:21]