Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Journal of Discrete Algorithms
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
An O*(1.0977n) exact algorithm for MAX INDEPENDENT SET in sparse graphs
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Discrete Applied Mathematics
Further improvement on maximum independent set in degree-4 graphs
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Maximum independent set in graphs of average degree at most three in O(1.08537n)
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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We first propose a new method, called “bottom-up method”, that, informally, “propagates” improvement of the worst-case complexity for “sparse” instances to “denser” ones and we show an easy though non-trivial application of it to the min set cover problem. We then tackle max independent set. Following the bottom-up method we propagate improvements of worst-case complexity from graphs of average degree d to graphs of average degree greater than d. Indeed, using algorithms for max independent set in graphs of average degree 3, we tackle max independent set in graphs of average degree 4, 5 and 6. Then, we combine the bottom-up technique with measure and conquer techniques to get improved running times for graphs of maximum degree 4, 5 and 6 but also for general graphs. The best computation bounds obtained for max independent set are O*(1.1571n), O*(1.1918n) and O*(1.2071n), for graphs of maximum (or more generally average) degree 4, 5 and 6 respectively, and O*(1.2127n) for general graphs. These results improve upon the best known polynomial space results for these cases.