Optimal induced universal graphs and adjacency labeling for trees

Publikation: Bidrag til bog/antologi/rapportKonferencebidrag i proceedingsForskningfagfællebedømt

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).
OriginalsprogEngelsk
Titel2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS)
Antal sider16
ForlagIEEE
Publikationsdato2015
Sider1311-1326
DOI
StatusUdgivet - 2015
BegivenhedThe Annual Symposium on Foundations of Computer Science - DoubleTree Hotel, Berkeley, California, USA
Varighed: 18 okt. 201520 okt. 2015
Konferencens nummer: 56

Konference

KonferenceThe Annual Symposium on Foundations of Computer Science
Nummer56
LokationDoubleTree Hotel
LandUSA
ByBerkeley, California
Periode18/10/201520/10/2015
NavnSymposium on Foundations of Computer Science. Annual Proceedings
ISSN1523-8288

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