Computability of Width of Submodular Partition Functions
نویسنده
چکیده
The notion of submodular partition functions generalizes many of well-known tree decompositions of graphs. For fixed k, there are polynomial-time algorithms to determine whether a graph has treewidth, branch-width, etc. at most k. Contrary to these results, we show that there is no sub-exponential algorithm for determining whether the width of a given submodular partition function is at most two. On the other hand, we show that for a subclass of submodular partition functions, which contains tree-width, there exists a polynomial-time algorithm that decides whether the width is at most k.
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