Optimal induced universal graphs and adjacency labeling for trees

TY - GEN

T1 - Optimal induced universal graphs and adjacency labeling for trees

AU - Alstrup, Stephen

AU - Dahlgaard, Søren

AU - Knudsen, Mathias Bæk Tejs

N1 - Conference code: 56

PY - 2015/12/11

Y1 - 2015/12/11

N2 - We show that there exists a graph G with O(n) nodes, where any forest of n nodes is a node-induced subgraph of G. Furthermore, for constant arboricity k, the result implies the existence of a graph with O(nk) nodes that contains all n-node graphs as node-induced subgraphs, matching a Ω(nk) lower bound. The lower bound and previously best upper bounds were presented in Alstrup and Rauhe (FOCS'02). Our upper bounds are obtained through a log2 n + O(1) labeling scheme for adjacency queries in forests. We hereby solve an open problem being raised repeatedly over decades, e.g. in Kannan, Naor, Rudich (STOC 1988), Chung (J. of Graph Theory 1990), Fraigniaud and Korman (SODA 2010).

AB - We show that there exists a graph G with O(n) nodes, where any forest of n nodes is a node-induced subgraph of G. Furthermore, for constant arboricity k, the result implies the existence of a graph with O(nk) nodes that contains all n-node graphs as node-induced subgraphs, matching a Ω(nk) lower bound. The lower bound and previously best upper bounds were presented in Alstrup and Rauhe (FOCS'02). Our upper bounds are obtained through a log2 n + O(1) labeling scheme for adjacency queries in forests. We hereby solve an open problem being raised repeatedly over decades, e.g. in Kannan, Naor, Rudich (STOC 1988), Chung (J. of Graph Theory 1990), Fraigniaud and Korman (SODA 2010).

U2 - 10.1109/FOCS.2015.84

DO - 10.1109/FOCS.2015.84

M3 - Article in proceedings

T3 - Symposium on Foundations of Computer Science. Annual Proceedings

SP - 1311

EP - 1326

BT - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS)

PB - IEEE

T2 - The Annual Symposium on Foundations of Computer Science

Y2 - 18 October 2015 through 20 October 2015

ER -