Document Type


Publication Date



Department of Computer Science


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.

Publisher's Statement

© Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu; licensed under Creative Commons License CC-BY 31st International Symposium on Algorithms and Computation (ISAAC 2020). Publisher’s version of record:

Publication Title

DROPS Dagstuhl Research Online Publication Server

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.


Publisher's PDF



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.