# Constructing labeling schemes through universal matrices

Amos Korman, David Peleg, Yoav Rodeh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

## Abstract

Let f be a function on pairs of vertices. An f-labeling scheme for a family of graphs labels the vertices of all graphs in such that for every graph and every two vertices u,v G, f(u,v) can be inferred by merely inspecting the labels of u and v. The size of a labeling scheme is the maximum number of bits used in a label of any vertex in any graph in . This paper illustrates that the notion of universal matrices can be used to efficiently construct f-labeling schemes. Let be a family of connected graphs of size at most n and let denote the collection of graphs of size at most n, such that each graph in is composed of a disjoint union of some graphs in . We first investigate methods for translating f-labeling schemes for to f-labeling schemes for . In particular, we show that in many cases, given an f-labeling scheme of size g(n) for a graph family , one can construct an f-labeling scheme of size g(n)+loglogn+O(1) for . We also show that in several cases, the above mentioned extra additive term of loglogn+O(1) is necessary. In addition, we show that the family of n-node graphs which are unions of disjoint circles enjoys an adjacency labeling scheme of size logn+O(1). This illustrates a non-trivial example showing that the above mentioned extra additive term is sometimes not necessary. We then turn to investigate distance labeling schemes on the class of circles of at most n vertices and show an upper bound of 1.5logn+O(1) and a lower bound of 4/3logn-O(1) for the size of any such labeling scheme. Keywords: Labeling schemes, Universal graphs, Universal matrices.

Original language English Algorithms and Computation - 17th International Symposium, ISAAC 2006, Proceedings 409-418 10 https://doi.org/10.1007/11940128_42 Published - 2006 Yes 17th International Symposium on Algorithms and Computation, ISAAC 2006 - Kolkata, IndiaDuration: 18 Dec 2006 → 20 Dec 2006

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4288 LNCS 0302-9743 1611-3349

### Conference

Conference 17th International Symposium on Algorithms and Computation, ISAAC 2006 India Kolkata 18/12/06 → 20/12/06

## Keywords

• Labeling schemes
• Universal graphs
• Universal matrices

## ASJC Scopus subject areas

• Theoretical Computer Science
• General Computer Science

## Fingerprint

Dive into the research topics of 'Constructing labeling schemes through universal matrices'. Together they form a unique fingerprint.