We present a bottom-up parsing algorithm for stochastic context-free grammars that is able (1) to deal with multiple interpretations of sentences containing compoundwords; (2) to extract N-most probableparses in O(n3) and computeat the same time all possible parses of any portionof the input sequence with their probabilities; (3) to deal with out of vocabulary words. Explicitly extracting all the parse trees associated to a given input sentence depends on the complexity of the grammar, but even in the case where this number is exponential in n, the chart used by the algorithm for the representation is of O(n2) space complexity.