Computability of Width of Submodular Partition Functions

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.

• Type: Conference
• Year: 2009
• Where: IWOCA
• Authors: Petr Skoda
• Keywords: Algorithms, IWOCA 2009, Polynomial-time Algorithm, Submodular Partition Functions, Well-known Tree Decompositions