Approximating clique-width and branch-width

We construct a polynomial-time algorithm to approximate the branch-width of certain symmetric submodular functions, and give two applications. The first is to graph "clique-width". Clique-width is a measure of the difficulty of decomposing a graph in a kind of tree-structure, and if a graph has clique-width at most k then the corresponding decomposition of the graph is called a "k-expression". We find (for fixed k) an O(n9 log n)-time algorithm that, with input an n-vertex graph, outputs either a (23k+2 - 1)

• Type: Journal
• Year: 2006
• Where: JCT
• Authors: Sang-il Oum, Paul D. Seymour
• Keywords: Clique-width, JCT 2006, Polynomial-time Algorithm, Symmetric Submodular Functions