The Power of Local Information in PageRank
Marco Bressan, Enoch Peserico, and Luca Pretto

TL;DR
This paper investigates the amount of local graph exploration needed to accurately rank nodes by PageRank, revealing that the required queries depend on the exploration model and correctness guarantees, with some algorithms needing nearly full graph exploration.
Contribution
The paper provides tight bounds on the number of queries needed for PageRank ranking under various exploration models, extending previous results and covering different query types.
Findings
Deterministic and Las Vegas algorithms require nearly full graph exploration in worst case.
Monte Carlo algorithms can perform significantly fewer queries if allowed local and random access.
Bounds generalize and improve upon previous results, applicable to PageRank approximation.
Abstract
How large a fraction of a graph must one explore to rank a small set of nodes according to their PageRank scores? We show that the answer is quite nuanced, and depends crucially on the interplay between the correctness guarantees one requires and the way one can access the graph. On the one hand, assuming the graph can be accessed only via "natural" exploration queries that reveal small pieces of its topology, we prove that deterministic and Las Vegas algorithms must in the worst case perform queries and explore essentially the entire graph, independently of the specific types of query employed. On the other hand we show that, depending on the types of query available, Monte Carlo algorithms can perform asymptotically better: if allowed to both explore the local topology around single nodes and access nodes at random in the graph they need queries in the…
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Taxonomy
TopicsData Management and Algorithms · Optimization and Search Problems · Graph Theory and Algorithms
