Optimal distance labeling schemes for trees

O Freedman, P Gawrychowski, PK Nicholson… - Proceedings of the …, 2017 - dl.acm.org
Labeling schemes seek to assign a short label to each node in a network, so that a function
on two nodes (such as distance or adjacency) can be computed by examining their labels …

Labeling schemes for small distances in trees

S Alstrup, P Bille, T Rauhe - SIAM Journal on Discrete Mathematics, 2005 - SIAM
We consider labeling schemes for trees, supporting various relationships between nodes at
small distance. For instance, we show that given a tree T and an integer k we can assign …

Distance labeling schemes for trees

S Alstrup, IL Gørtz, EB Halvorsen, E Porat - arXiv preprint arXiv …, 2015 - arxiv.org
We consider distance labeling schemes for trees: given a tree with $ n $ nodes, label the
nodes with binary strings such that, given the labels of any two nodes, one can determine …

Approximate distance labeling schemes

C Gavoille, M Katz, NA Katz, C Paul… - Algorithms—ESA 2001: 9th …, 2001 - Springer
We consider the problem of labeling the nodes of an n-node graph G with short labels in
such a way that the distance between any two nodes u, v of G can be approximated …

Near-optimal labeling schemes for nearest common ancestors

S Alstrup, EB Halvorsen, KG Larsen - Proceedings of the Twenty-Fifth Annual …, 2014 - SIAM
We consider NCA labeling schemes: given a rooted tree T, label the nodes of T with binary
strings such that, given the labels of any two nodes, one can determine, by looking only at …

Short and simple labels for small distances and other functions

H Kaplan, T Milo - Algorithms and Data Structures: 7th International …, 2001 - Springer
We present a labeling scheme for rooted trees which allows to compute, from the label ofv
alone, unique identifiers for the ancestors of v that are at distance at most d from v. For any …

Forbidden-set distance labels for graphs of bounded doubling dimension

I Abraham, S Chechik, C Gavoille, D Peleg - Proceedings of the 29th …, 2010 - dl.acm.org
The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling
dimension bounded by α. For an n-vertex graph G in this family, and for any desired …

A note on exact distance labeling

O Weimann, D Peleg - Information processing letters, 2011 - Elsevier
We show that the vertices of an edge-weighted undirected graph can be labeled with labels
of size O (n) such that the exact distance between any two vertices can be inferred from their …

Constructing labeling schemes through universal matrices

A Korman, D Peleg, Y Rodeh - International Symposium on Algorithms …, 2006 - Springer
Let f be a function on pairs of vertices. An f-labeling scheme for a family of graphs \mathcalF
labels the vertices of all graphs in \mathcalF such that for every graph G∈\mathcalF and …

Distance labeling in graphs

C Gavoille, D Peleg, S Pérennes, R Raz - Journal of algorithms, 2004 - Elsevier
We consider the problem of labeling the nodes of a graph in a way that will allow one to
compute the distance between any two nodes directly from their labels (without using any …