Compact Forbidden-Set Routing

We study labelling schemes for X-constrained path problems. Given a graph (V,E) and X ⊆ V , a path is X-constrained if all intermediate vertices avoidX. We study the problem of assigning labels J(x) to vertices so that given {J(x) : x ∈ X} for any X ⊆ V , we can route on the shortest X-constrained path between x, y ∈ X. This problem is motivated by Internet routing, where the presence of routing policies means that shortest-path routing is not appropriate. For graphs of tree width k, we give a routing scheme using routing tables of size O(k log n). We introduce m-clique width, generalizing clique width, to show that graphs of m-clique width k also have a routing scheme using size O(k log n) tables.