Exact Algorithms for Maximum Independent Set

We show that the maximum independent set problem (MIS) on an n-vertex graph can be solved in 1.2002 n n O(1) time and polynomial space, which is even faster than Robson’s 1.2109 n n O(1)-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7. Our algorithms are obtained by effectively using fast algorithms for MIS in low-degree graphs and making careful analyses for MIS in high-degree graphs.

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