Multi-Clique-Width, a Powerful New Width Parameter
Multi-clique-width is a width parameter for graphs. It is obtained by a simple modification in the definition of clique-width. It has the advantage of providing a natural extension of tree-width. Unlike clique-width, it does not explode exponentially compared to tree-width. Efficient algorithms based on multi-clique-width are still possible for interesting tasks like computing the size of a maximum independent set (or even the independent set polynomial) or computing the chromatic number. For these tasks, the running time as a function of the multi-clique-width is the same as the running time of the fastest known algorithm as a function of the clique-width. This results in an exponential speed-up for some graphs, if the corresponding graph generating expressions are given. The reason is that the multi-clique-width is never bigger, but is exponentially smaller than the clique-width for many graphs.
Tree-width and clique-width will be introduced.
Based on the ITCS 2017 paper: "Multi-Clique-Width."