  We present the first succinct distance oracles for (unweighted) interval
graphs and related classes of graphs, using a novel succinct data structure for
ordinal trees that supports the mapping between preorder (i.e., depth-first)
ranks and level-order (breadth-first) ranks of nodes in constant time. Our
distance oracles for interval graphs also support navigation queries -- testing
adjacency, computing node degrees, neighborhoods, and shortest paths -- all in
optimal time. Our technique also yields optimal distance oracles for proper
interval graphs (unit-interval graphs) and circular-arc graphs. Our tree data
structure supports all operations provided by different approaches in previous
work, as well as mapping to and from level-order ranks and retrieving the last
(first) internal node before (after) a given node in a level-order traversal,
all in constant time.
