Compact Navigation Oracles for Graphs with Bounded Clique-Width

The notion of clique-width for graphs is a relatively new topic which has received attention in the past decade. A graph has bounded clique-width if it can be represented as an algebraic expression on a constant number of labels associated with its vertices. Many computationally hard problems can be solved in polynomial time for graphs with bounded clique-width. Interestingly also, many graph families that arise in practice have bounded clique-width. In this paper, we present compact navigation oracles for graphs with bounded clique-width. Our oracles answer adjacency and neighborhood queries in constant time using O(n) space (i.e., O(n) bits) for a graph of size n, and report the degree of each given vertex, also in constant time, using O(n lg lg n) bits.