Despite decades of research, effective treatments for most cancers remain elusive. One reason is that different instances of cancer result from different combinations of multiple genetic mutations (hits). Therefore, treatments that may be effective in some cases are not effective in others. We previously developed an algorithm for identifying combinations of carcinogenic genes with mutations (multi-hit combinations), which could suggest a likely cause for individual instances of cancer. Most cancers are estimated to require three or more hits. However, the computational complexity of the algorithm scales exponentially with the number of hits, making it impractical for identifying combinations of more than two hits. To identify combinations of greater than two hits, we used a compressed binary matrix representation, and optimized the algorithm for parallel execution on an NVIDIA V100 graphics processing unit (GPU). With these enhancements, the optimized GPU implementation was on average an estimated 12,144 times faster than the original integer matrix based CPU implementation, for the 3-hit algorithm, allowing us to identify 3-hit combinations. The 3-hit combinations identified using a training set were able to differentiate between tumor and normal samples in a separate test set with 90% overall sensitivity and 93% overall specificity. We illustrate how the distribution of mutations in tumor and normal samples in the multi-hit gene combinations can suggest potential driver mutations for further investigation. With experimental validation, these combinations may provide insight into the etiology of cancer and a rational basis for targeted combination therapy. Cancer is one of the leading causes of death in the US with a projected 606,880 deaths in 2019 1. Despite significant progress, effective treatment in advanced cases remain elusive, with most progress coming from prevention and early detection 2,3. One of many possible reasons is that, although cancer is known to be caused primarily by multiple genetic mutations 4-9 , we cannot in general determine the specific combination of mutations responsible for a given instance of cancer 10,11. Knowing the specific combination of hits in individual cases would allow us to develop more effective targeted combination therapies 10,11. Although there are other factor that may contribute to cancer growth, such as tumor microenvironment, epigenetic modifications, gene fusion, germline defects, etc., the focus of this work is on somatic mutations 12-18. Current computational approaches search for cancer genes and mutations that increase cancer risk (the probability of getting cancer) 18-29. In addition to other considerations, these methods search for genes that are significantly more frequently mutated in tumor samples compared to an estimated background mutation rate. However, mutations in any one of these genes by themselves do not always result in cancer, suggesting that carcinogenesis may require additional mutations, as illustrated by the following exmples. Germline mut...