Large-scale cancer genomics projects are providing a large volume of data about genomic, epigenomic and gene expression aberrations in multiple cancer types. One of the remaining challenges is to identify driver mutations, driver genes and driver pathways promoting cancer proliferation and filter out the unfunctional and passenger ones. In this study, we propose two methods to solve the so-called maximum weight submatrix problem, which is designed to de novo identify mutated driver pathways from mutation data in cancer. The first one is an exact method that can be helpful for assessing other approximate or/and heuristic algorithms. The second one is a stochastic and flexible method that can be employed to incorporate other types of information to improve the first method. Particularly, we propose an integrative model to combine mutation and expression data. We first apply our methods onto simulated data to show their efficiency. We further apply the proposed methods onto several real biological datasets, showing that our integrative model can identify more biologically relevant gene sets. We further propose an exact mathematical programming method de novo identify co-occurring mutated driver pathways (CoMDP) in carcinogenesis without any prior information beyond mutation profiles. Two possible properties of mutations that occurred in cooperative pathways were exploited to achieve this: (1) each individual pathway has high coverage and high exclusivity; and (2) the mutations between the pair of pathways showed statistically significant co-occurrence. The efficiency of CoMDP was validated first by testing on simulated data and comparing it with a previous method. Then CoMDP was applied to several real biological datasets.