Exact algorithms for maximum independent set

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 de...

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Vydáno v:Information and computation Ročník 255; s. 126 - 146
Hlavní autoři: Xiao, Mingyu, Nagamochi, Hiroshi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.08.2017
Témata:
Amortized analysis
Branch-and-reduce
Exact algorithm
Graph
Independent set
Measure-and-conquer
Polynomial-space
Graph
Amortized analysis
Independent set
Measure-and-conquer
Exact algorithm
Branch-and-reduce
Polynomial-space
ISSN:0890-5401, 1090-2651
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Shrnutí: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2017.06.001