Exact algorithms for maximum independent set

We show that the maximum independent set problem on an n-vertex graph can be solved in 1.1996(n)n(0)(1) time and polynomial space, which even is faster than Robson's 1.2109(n)n(0)(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 1.1893(n)n(0)(1) and 1.1970(n)n(0)(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. (C) 20 17 Elsevier Inc. All rights reserved.