# Sublinear-Space Distance Labeling Using Hubs

@inproceedings{Gawrychowski2016SublinearSpaceDL,
title={Sublinear-Space Distance Labeling Using Hubs},
author={Pawel Gawrychowski and Adrian Kosowski and Przemysław Uznański},
booktitle={DISC},
year={2016}
}
• Published in DISC 22 July 2015
• Computer Science
A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. We propose a series of new labeling schemes within the framework of so-called hub labeling (HL, also known as landmark labeling or 2-hop-cover labeling), in which each node $u$ stores its distance to all nodes from an appropriately chosen set of hubs $S(u) \subseteq V$. For a queried pair of…
12 Citations
Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling
• Computer Science
PODC
• 2019
A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their
A note on distance labeling in planar graphs
• Computer Science
ArXiv
• 2016
It is shown that, in fact, labels of length $O(\sqrt{n})$ are enough.
Shorter Labeling Schemes for Planar Graphs
• Mathematics, Computer Science
SODA
• 2020
This work designs a labeling scheme with labels of bit length that generalizes to graphs of bounded Euler genus with the same label length up to a second-order term, improving the previous best upper bound of $n^{2+o(1)}$.
Exact Distance Oracles Using Hopsets
• Computer Science, Mathematics
ArXiv
• 2018
It is shown that $3-hopsets require exponentially fewer shortcuts per node than any previously described distance oracle while incurring only a quadratic increase in the query decoding time, and actually offer a speedup when compared to simple oracles based on a direct application of$2-hopset.
Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond
• Computer Science, Mathematics
ICALP
• 2019
It is shown that $3-hopsets require exponentially fewer shortcuts per node than any previously described distance oracle while incurring only a quadratic increase in the query decoding time, and actually offer a speedup when compared to simple oracles based on a direct application of$2-hopset.
Labeling Schemes for Nearest Common Ancestors through Minor-Universal Trees
• Computer Science
SODA
• 2018
It is argued that the existing schemes can be reformulated as such, and it allows us to obtain clean and good bounds on the length of the labels, and shows that the size of any minor-universal tree for trees on $n$ nodes is $\Omega(n^{2.174})$.
Shorter Labels for Routing in Trees
• Computer Science
SODA
• 2021
The first (and significant) progress is made in 19 years on determining the correct second-order term for the length of a label in a routing labeling scheme for trees on $n$ nodes with labels of length $\log n+O((\log\log n)^{2})$.
Near-Optimal Distance Emulator for Planar Graphs
• Computer Science, Mathematics
ESA
• 2018
The result implies that, on any unweighted undirected planar graph, one can compute all-pairs shortest path distances among $k$ terminals in $\tilde O(n)$ time when $k=O(n^{1/3})$.
Efficient Labeling for Reachability in Digraphs
• Computer Science
ArXiv
• 2020
This work considers labeling nodes of a directed graph for reachability queries and designs a scheme with labels consisting of $n/3+o(n)$ bits, which is optimal, up to the lower order term.
Efficient Labeling for Reachability in Directed Acyclic Graphs
• Computer Science
ISAAC
• 2020
This work considers labeling nodes of a directed graph for reachability queries, and extends Munro and Nicholson's approach to obtain a scheme with labels consisting of n/3 + o(n) bits.

## References

SHOWING 1-10 OF 28 REFERENCES
Sublinear distance labeling for sparse graphs
• Computer Science, Mathematics
ArXiv
• 2015
This paper presents the first distance labeling scheme of size opnq for sparse graphs (and hence bounded degree graphs) and separates the complexity from general graphs which require pnq size Moon.
Simpler, faster and shorter labels for distances in graphs
• Computer Science
SODA
• 2016
This paper presents a simple algorithm with shorter labels and shorter query time than any previous solution, thereby improving the state-of-the-art with respect to both label length and query time in one single algorithm.
Distance labeling in graphs
• Computer Science, Mathematics
SODA '01
• 2001
A note on exact distance labeling
• Computer Science
Inf. Process. Lett.
• 2011
On compact representations of All-Pairs-Shortest-Path-Distance matrices
• Computer Science, Mathematics
Theor. Comput. Sci.
• 2008
On Approximate Distance Labels and Routing Schemes with Affine Stretch
• Computer Science, Mathematics
DISC
• 2011
The construction provides distance labels with affine stretch of (2k - 2)d+1 which is better than the stretch (2K - 1)d scheme of Thorup and Zwick and a compact routing scheme with poly-logarithmic addresses that provides affine Stretch guarantees.
Reachability and distance queries via 2-hop labels
• Computer Science
SODA '02
• 2002
The proposed data structure for representing all distances in a graph is distributed in the sense that it may be viewed as assigning labels to the vertices, such that a query involving vertices u and v may be answered using only the labels of u andV.
Additive Spanners and Distance and Routing Labeling Schemes for Hyperbolic Graphs
• Computer Science, Mathematics
Algorithmica
• 2010
Using the Layering Partition technique, it is shown that every n-vertex δ-hyperbolic graph with δ≥1/2 has an additive O(δlog n)-spanner with at most O( δn) edges and provide a simpler, in this paper, and faster construction of distance approximating trees ofδ- hyperbolic graphs with an additive error O( Δlog’n).
On the hardness of distance oracle for sparse graph
• Computer Science, Mathematics
ArXiv
• 2010
It is shown that if one can build distance oracle for sparse graph G=(V,E), which requires s(|V|,|E|) space and answers a (2-\epsilon,c)-approximate distance query in time t(| V|, |E|), then, set-intersection can be solved in t(m+|U|,n) time using s( m+| U|, n) space.
Distance Oracles beyond the Thorup-Zwick Bound
• Computer Science, Mathematics
2010 IEEE 51st Annual Symposium on Foundations of Computer Science
• 2010
It is shown that a 2-approximate distance oracle requires space $\tOmega(n^2 / \sqrt{\alpha})$ and this implies a space lower bound to achieve approximation $2d+1$.