De Novo Peptide Sequencing Based on Vertex Contraction Algorithm

De novo peptide sequencing is an important method for peptide sequencing and protein identification. It can be transformed into a special case of paths avoiding forbidden pairs problem (PAFP). General PAFP is NP-complete. The definition of PAFP is the following: Given a directed acyclic graph G = (V, E), two distinguished vertices source s, sink t ∈ V , a set of forbidden pairs F ⊂ V × V, and an edge weight function w : E -+ R, asking for a maximum weight path from s to t passing at most one vertex from each forbidden pair. In the process of transformation from de novo peptide sequencing to PAFP, forbidden pairs have nested structure. We give a vertex contraction algorithm which is designed based on nested structure of forbidden pairs to solve paths avoiding forbidden pairs problem. The time complexity of vertex contraction algorithm is O(|V|³).