Favorable graph decomposition for dense graphs to solve independent set problem I have to solve an independent set problem (ISP) on dense graphs with many cliques. To tackle the problem, I'm considering to use graph decompositions such as tree-, modular decomposition or clique-width k-expression trees. 

Are there some decompositions (or other techniques) favorable for my type of graphs?

From what I understand, considering e.g. the tree-decomposition, the ISP can be solved in $\mathcal{O}(n2^k)$ where $n$ is number of vertices of the tree and $k$ the tree-width. Moreover, the tree-width is a measure of how similar a graph is to a tree. From this, I concluded that a graph which is not very similar to tree (maybe just like mine) has a large tree-width and, hence, the tree-decomposition is maybe not a favorable decomposition to solve the ISP.

Is e.g. the clique-width k-expression tree more suitable for my case?
The problem is that most decompositions (I know of) are themselves much harder to compute/approximate than INDEPENDENT SET.

However, if your graphs are really very dense, their complements might be sparse. Thus, it might be worth considering solving CLIQUE in the complement of the input graph. This can be done in $O(nd\cdot 1.45^d)$ time (Eppstein, Löffler, Strash), where $d$ is the degeneracy of the input graph (which is even smaller than the treewidth).