De novo sequencing is one of the most promising proteomics techniques for identification of protein posttranslation modifications (PTMs) in studying protein regulations and functions. We have developed a computer tool PRIME for identification of b and y ions in tandem mass spectra, a key challenging problem in de novo sequencing. PRIME utilizes a feature that ions of the same and different types follow different mass-difference distributions to separate b from y ions correctly. We have formulated the problem as a graph partition problem. A linear integer-programming algorithm has been implemented to solve the graph partition problem rigorously and efficiently. The performance of PRIME has been demonstrated on a large amount of simulated tandem mass spectra derived from Yeast genome and its power of detecting PTMs has been tested on 216 simulated phosphopeptides.