  In this paper, we introduce an exact algorithm with a time complexity of
$O^*(1.325^m)$ for the {\sc weighted mutually exclusive maximum set cover}
problem, where $m$ is the number of subsets in the problem. This is an NP-hard
motivated and abstracted from a bioinformatics problem of identifying signaling
pathways based gene mutations. Currently, this problem is addressed using
heuristic algorithms, which cannot guarantee the performance of the solution.
By providing a relatively efficient exact algorithm, our approach will like
increase the capability of finding better solutions in the application of
cancer research.
