Cancer arises from combinations of somatic mutations (hits), and identifying these combinations is critical for understanding carcinogenesis and enabling targeted therapies. This task can be formulated as a weighted set cover problem, yet exhaustive enumeration leads to exponential search space growth as the number of hits increases, limiting prior enumeration-based work to at most 5-hit combinations even on large-scale supercomputers. We propose a novel algorithm that decomposes higher-order combinations through a shortest addition chain and formulates sample coverage computation as matrix multiplication. It employs a robust score-bounded search strategy that eliminates unpromising candidates without evaluation, while guaranteeing that the best-scoring combination is never discarded. Experiments show our method visits less than one-millionth of prior search spaces, identifies 4-hit combinations in about 5 seconds on a single GPU, outperforms thousand-node supercomputers by orders of magnitude, and extends practical reach of enumeration-based cancer screening from 5-hit to 9-hit combinations.