# Massively Parallel Single-Source SimRanks in o(log n) Rounds

arXiv: https://arxiv.org/abs/2304.04015 · HTML: https://mlsanity.com/paper/2304.04015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [SIGMA: An Efficient Heterophilous Graph Neural Network with Fast Global Aggregation](https://mlsanity.com/paper/2305.09958/) (2023)

## Abstract (arXiv)

SimRank is one of the most fundamental measures that evaluate the structural similarity between two nodes in a graph and has been applied in a plethora of data management tasks. These tasks often involve single-source SimRank computation that evaluates the SimRank values between a source node s and all other nodes. Due to its high computation complexity, single-source SimRank computation for large graphs is notoriously challenging, and hence recent studies resort to distributed processing. To our surprise, although SimRank has been widely adopted for two decades, theoretical aspects of distributed SimRanks with provable results have rarely been studied. In this paper, we conduct a theoretical study on single-source SimRank computation in the Massive Parallel Computation (MPC) model, which is the standard theoretical framework modeling distributed systems such as MapReduce, Hadoop, or Spark. Existing distributed SimRank algorithms enforce either Omega(log n) communication round complexity or Omega(n) machine space for a graph of n nodes. We overcome this barrier. Particularly, given a graph of n nodes, for any query node v and constant error ε>frac3n, we show that using O(log2 log n) rounds of communication among machines is almost enough to compute single-source SimRank values with at most ε absolute errors, while each machine only needs a space sub-linear to n. To the best of our knowledge, this is the first single-source SimRank algorithm in MPC that can overcome the Theta(log n) round complexity barrier with provable result accuracy.