A Simple Distributed Algorithm for Sparse Fractional Covering and Packing Problems

TL;DR

This paper introduces a simple distributed algorithm in the CONGEST model that efficiently approximates sparse fractional covering and packing problems, improving upon previous methods in simplicity and epsilon dependency.

Contribution

The paper proposes a new distributed algorithm that simplifies previous approaches and enhances approximation efficiency for sparse fractional covering and packing problems.

Findings

Achieves a (1+ε)-approximation in the CONGEST model.

Simplifies the algorithmic approach compared to prior work.

Significantly improves epsilon dependency in approximation.

Abstract

This paper presents a distributed algorithm in the CONGEST model that achieves a $(1+\epsilon)$-approximation for row-sparse fractional covering problems (RS-FCP) and the dual column-sparse fraction packing problems (CS-FPP). Compared with the best-known $(1+\epsilon)$-approximation CONGEST algorithm for RS-FCP/CS-FPP developed by Kuhn, Moscibroda, and Wattenhofer (SODA'06), our algorithm is not only much simpler but also significantly improves the dependency on $\epsilon$.