We consider the problem 2-Dim-Bounding-Surface. 2-Dim-Bounded-Surface asks whether or not there is a subcomplex $S$ of a simplicial complex $K$ homeomorphic to a given compact, connected surface bounded by a given subcomplex $B\subset K$. 2-Dim-Bounding-Surface is NP-hard. We show it is fixed-parameter tractable with respect to the treewidth of the 1-skeleton of the simplicial complex $K$. Using some of the techniques we developed for the 2-Dim-Bounded-Surface problem, we obtain fixed parameter tractable algorithms for other topological problems such as computing an optimal chain with a given boundary and computing an optimal chain in a given homology class.
翻译：我们考虑的是2-Dim-Bound-Surface的问题。 2-Dim-Bound-Surface问是否有一个亚复合物美元S$S的亚合成物,它是一个简单的复合体,它与一个特定的亚复合体($B\subset K$)。 2-Dim-Bound-Surface是硬的NP。我们表明它相对于一个简单的复合体($K)的1-sketon的树枝是固定的参数可移动的。我们利用我们为2-Dim-Bound-Surface问题开发的一些技术,我们获得了一个固定参数可移动的算法,以处理其他的地形问题,例如用一个特定的边界计算一个最佳链,并在一个给定的同族类中计算一个最佳链。
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