We study the tractability of the maximum independent set problem from the viewpoint of graph width parameters, with the goal of defining a width parameter that is as general as possible and allows to solve independent set in polynomial-time on graphs where the parameter is bounded. We introduce two new graph width parameters: one-sided maximum induced matching-width (o-mim-width) and neighbor-depth. O-mim-width is a graph parameter that is more general than the known parameters mim-width and tree-independence number, and we show that independent set and feedback vertex set can be solved in polynomial-time given a decomposition with bounded o-mim-width. O-mim-width is the first width parameter that gives a common generalization of chordal graphs and graphs of bounded clique-width in terms of tractability of these problems. The parameter o-mim-width, as well as the related parameters mim-width and sim-width, have the limitation that no algorithms are known to compute bounded-width decompositions in polynomial-time. To partially resolve this limitation, we introduce the parameter neighbor-depth. We show that given a graph of neighbor-depth $k$, independent set can be solved in time $n^{O(k)}$ even without knowing a corresponding decomposition. We also show that neighbor-depth is bounded by a polylogarithmic function on the number of vertices on large classes of graphs, including graphs of bounded o-mim-width, and more generally graphs of bounded sim-width, giving a quasipolynomial-time algorithm for independent set on these graph classes. This resolves an open problem asked by Kang, Kwon, Str{\o}mme, and Telle [TCS 2017].

翻译：我们从图形宽度参数的角度研究最大独立设置问题的可感性。 我们的目标是从图形宽度参数的角度来研究最大独立设置问题的可感性。 我们的目标是定义一个尽可能普遍的宽度参数, 并允许在参数受约束的图形上解压缩多角度时独立设置。 我们引入两个新的图形宽度参数: 单向最大诱导匹配宽度( o- mim- width) 和邻居深度。 O- mim- width 是比已知参数 mim- width 和树独立数更普通的图形参数。 我们显示, 独立的数据集和反馈顶端的顶端参数可以在多层次的多层次中解析。 O- mim-wid是第一个宽度参数, 在这些问题的可感光度方面, 直径直径的直径直径直径的直径直径直位值上, 直径直径直流的直径直径直径直径直径直径直径直的直径直位数。