We show that the maximum independent set problem (MIS) 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 analyses on the structure of bounded-degree graphs