Massively Parallel Approximate Distance Sketches

TL;DR

This paper develops efficient algorithms for constructing approximate distance sketches in the MPC model, enabling faster distance estimation and shortest path computations in large-scale distributed systems.

Contribution

It introduces new MPC algorithms for optimal and near-optimal distance sketches, and demonstrates their application to compute hopsets and approximate shortest paths.

Findings

Constructed stretch/space optimal distance sketches in polylogarithmic rounds.

Developed faster algorithms with higher stretch but fewer rounds.

Enabled the first polylogarithmic time approximate shortest path algorithm in MPC.

Abstract

Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. We provide efficient constructions in both of these models, but our core results are for MPC. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm that constructs distance sketches with worse stretch but that only takes polylogarithmic rounds. Along the way, we show that other useful combinatorial structures can also be computed in MPC. In particular, one key component we use to construct distance sketches are an MPC construction of the hopsets of Elkin and Neiman (2016). This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.