This paper describes how a constraint dependency grammar (CDG) parser performs a syntactic analysis of a single sentence (as part of a speech recognition system). The paper extends an existing CDG (developed by H. Maruyama) to process a lattice or graph of sentence hypotheses instead of separate text strings. The paper also describes how the CDG algorithm is extended to process a word graph on a single processor machine. Two tables of data and four figures presenting aspects of the CDG algorithm are included. (RS)