Fast C-K-R Partitions of Sparse Graphs

TL;DR

This paper introduces efficient algorithms for creating probabilistic embeddings and approximate distance oracles specifically tailored for sparse graphs, leveraging a novel fast sampling method for probabilistic partitions.

Contribution

It provides a new fast sampling algorithm for probabilistic partitions in sparse graphs, enabling quicker construction of embeddings and distance oracles.

Findings

Achieves faster construction times for embeddings in sparse graphs

Provides probabilistic partitions with improved efficiency

Enables practical applications in large-scale sparse graph analysis

Abstract

We present fast algorithms for constructing probabilistic embeddings and approximate distance oracles in sparse graphs. The main ingredient is a fast algorithm for sampling the probabilistic partitions of Calinescu, Karloff, and Rabani in sparse graphs.