On Fine-Grained Exact Computation in Regular Graphs
Saeed Akhoondian Amiri
TL;DR
This paper proves that computing the maximum independent set exactly in regular graphs is computationally hard under ETH, and extends these results to related problems and specific graph classes.
Contribution
It establishes new complexity lower bounds for maximum independent set and related problems in regular graphs, including planar cases.
Findings
No subexponential algorithm for MIS in d-regular graphs unless ETH fails
Lower bounds for vertex cover and clique problems in regular graphs
NP-hardness of MIS in 5-regular planar graphs
Abstract
We show that there is no subexponential time algorithm for computing the exact solution of the maximum independent set problem in d-regular graphs unless ETH fails. We expand our method to show that it helps to provide lower bounds for other covering problems such as vertex cover and clique. We utilize the construction to show the NP-hardness of MIS on 5-regular planar graphs, closing the exact complexity status of the problem on regular planar graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Interconnection Networks and Systems