Abstract
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 tree-width, 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. In addition, we also develop another dual notion for submodular partition functions which is analogous to loose tangles for connectivity functions.
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Škoda, P. (2009). Computability of Width of Submodular Partition Functions. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_44
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DOI: https://doi.org/10.1007/978-3-642-10217-2_44
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