Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees
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.
Cite
@article{arxiv.2005.07644,
title = {Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees},
author = {Meng He and J. Ian Munro and Yakov Nekrich and Sebastian Wild and Kaiyu Wu},
journal= {arXiv preprint arXiv:2005.07644},
year = {2020}
}
Comments
to appear in ISAAC 2020