# Best of Two Local Models: Local Centralized and Local Distributed Algorithms

arXiv: https://arxiv.org/abs/1402.3796 · HTML: https://mlsanity.com/paper/1402.3796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2014.

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

- [Agnostic proper learning of monotone functions: beyond the black-box correction barrier](https://mlsanity.com/paper/2304.02700/) (2023)

## Abstract (arXiv)

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design improved centralized local algorithms for: maximal independent set, maximal matching, and an approximation scheme for maximum (weighted) matching over bounded degree graphs. The improvement is threefold: the algorithms are deterministic, stateless, and the number of probes grows polynomially in log^* n, where n is the number of vertices of the input graph. The recursive centralized local improvement technique by Nguyen and Onak~citeonak2008 is employed to obtain an improved distributed approximation scheme for maximum (weighted) matching. The improvement is twofold: we reduce the number of rounds from O(log n) to O(log^*n) for a wide range of instances and, our algorithms are deterministic rather than randomized.