Adjacency labeling schemes and induced-universal graphs

TY - GEN

T1 - Adjacency labeling schemes and induced-universal graphs

AU - Alstrup, Stephen

AU - Kaplan, Haim

AU - Thorup, Mikkel

AU - Zwick, Uri

N1 - Conference code: 47

PY - 2015/6/14

Y1 - 2015/6/14

N2 - We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

AB - We describe a way of assigning labels to the vertices of any undirected graph on up to n vertices, each composed of n/2+ O(1) bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an n/2+O(log n) bound of Moon. As a consequence, we obtain an induced-universal graph for n-vertex graphs containing only O(2n/2) vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs.

U2 - 10.1145/2746539.2746545

DO - 10.1145/2746539.2746545

M3 - Article in proceedings

SN - 978-1-4503-3536-2

SP - 625

EP - 634

BT - Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015

PB - Association for Computing Machinery

T2 - Annual ACM Symposium on the Theory of Computing 2015

Y2 - 15 June 2015 through 17 June 2015

ER -