An exact algorithm for maximum independent set in degree-5 graphs

Abstract

The maximum independent set problem is a basic NP-hard problem and has been extensively studied in exact algorithms. The maximum independent set problems in low-degree graphs are also important and may be bottlenecks of the problem in general graphs. In this paper, we present a $1.1736^n{n}^{O\left(1\right)}$-time exact algorithm for the maximum independent set problem in an $n$-vertex graph with degree bounded by $5$, improving the previous running time bound of $1.1895^n{n}^{O\left(1\right)}$. In our algorithm, we show that the graph after applying reduction rules always has a good local structure branching on which will effectively reduce the instance. Based on this, we obtain an improved algorithm without introducing a large number of branching rules.