Document Type
Article
Publication Date
2020
Department
Department of Computer Science
Abstract
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.
Publication Title
DROPS Dagstuhl Research Online Publication Server
Recommended Citation
He, M.,
Munro, J.,
Nekrich, Y.,
Wild, S.,
&
Wu, K.
(2020).
Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees.
DROPS Dagstuhl Research Online Publication Server,
25, 25:1-25:18.
http://doi.org/10.4230/LIPIcs.ISAAC.2020.25
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/16555
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Version
Publisher's PDF
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: https://doi.org/10.4230/LIPIcs.ISAAC.2020.25