Exact algorithms for maximum independent set

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Information and Computation, ISSN: 0890-5401, Vol: 255, Page: 126-146

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Mingyu Xiao; Hiroshi Nagamochi
Elsevier BV
Mathematics; Computer Science
article description
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.