Can one compute the pageRank score of a single, arbitrary node in a graph, exploring only a vanishing fraction of the graph? We provide a positive answer to this extensively researched open question. We develop the first algorithm that, for any n-node graph, returns a multiplicative (1±ϵ)-approximation of the score of any given node with probability (1−δ), using at most On2/3 ln(n)1/3 ln(1/δ)2/3ϵ−2/3 = Õ(n2/3) queries which return either a node chosen uniformly at random, or the list of neighbours of a given node. Alternatively, we show that the same guarantees can be attained by fetching at most OE4/5d−3/5 ln(n)1/5 ln(1/δ)3/5ϵ−6/5 = Õ(E4/5) arcs, where E is the total number of arcs in the graph and d is its average degree.

Brief announcement: On approximating pageRank locally with sublinear query complexity / M. Bressan, E. Peserico, L. Pretto - In: SPAA '18: Proceedings[s.l] : ACM, 2018. - ISBN 9781450357999. - pp. 87-89 (( Intervento presentato al 30. convegno SPAA tenutosi a Wien nel 2018 [10.1145/3210377.3210664].

### Brief announcement: On approximating pageRank locally with sublinear query complexity

#### Abstract

Can one compute the pageRank score of a single, arbitrary node in a graph, exploring only a vanishing fraction of the graph? We provide a positive answer to this extensively researched open question. We develop the first algorithm that, for any n-node graph, returns a multiplicative (1±ϵ)-approximation of the score of any given node with probability (1−δ), using at most On2/3 ln(n)1/3 ln(1/δ)2/3ϵ−2/3 = Õ(n2/3) queries which return either a node chosen uniformly at random, or the list of neighbours of a given node. Alternatively, we show that the same guarantees can be attained by fetching at most OE4/5d−3/5 ln(n)1/5 ln(1/δ)3/5ϵ−6/5 = Õ(E4/5) arcs, where E is the total number of arcs in the graph and d is its average degree.
##### Scheda breve Scheda completa Scheda completa (DC) Local computation; PageRank; Query complexity; Random walks; Sublinear algorithms
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/922288`
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