We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally treewidth-fragile graph classes, a property that is true for many natural graph classes with sublinear separators. We also provide quasipolynomial-time approximation schemes for these problems in all classes with sublinear separators.
翻译:我们给单调最大化问题提供多元时近似方案,从距离(直至固定的上下限)和在接缝树枝图中可有效溶解的单调最大化问题。这些方案适用于所有小树枝-易碎图类,对于许多具有亚线性分离器的自然图类来说,这是一个属性。我们还为使用亚线性分离器的所有分类提供这些问题的准极代近似方案。