We show that the maximum independent set problem on an n-vertex graph can be solved in 1.1996nnO(1) time and polynomial space, which even is faster than Robson's 1.2109nnO(1)-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of 1.1893nnO(1) and 1.1970nnO(1), respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analysis on the structure of bounded-degree graphs.
Xiao, M., & Nagamochi, H. (2017). Exact algorithms for maximum independent set. Information and Computation, 255, 126–146. https://doi.org/10.1016/j.ic.2017.06.001