Path-Reporting Distance Oracles for Vertex-Labeled Graphs
Ofer Neiman, Alon Spector

TL;DR
This paper introduces improved vertex-label distance oracles for weighted undirected graphs that are path-reporting and achieve near-optimal stretch, with efficient query time and manageable size.
Contribution
It develops a path-reporting vertex-label distance oracle with slightly increased stretch and size, and also improves the stretch to the optimal value with mild query time increase.
Findings
Path-reporting oracle with stretch (4k-5)(1+ε), size O(n^{1+o(1)}·ℓ^{1/k})
Oracle with stretch 2k-1, query time O(ℓ^{1/k}·log n), size O(k·n·ℓ^{1/k})
Addresses drawbacks of previous state-of-the-art results by balancing stretch, path-reporting, and efficiency.
Abstract
Let be a weighted undirected graph, with vertices. A distance oracle is a data structure that can quickly answer distance queries, with some stretch factor. A seminal work of \cite{TZ01}, given an integer , provides such an oracle with stretch , query time , and size . Furthermore, this oracle can also report a path in corresponding to the returned distance. In this paper we focus on vertex-labeled graphs, in which each vertex is given a label from a set of size . A {\em vertex-label distance oracle} answers queries of the form , where and , by reporting (an approximation to) the distance from to the closest vertex of label . Following \cite{HLWY11}, it was shown in \cite{C12} that for any integer , there exists a vertex-label distance oracle with stretch ,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
