# Almost Optimal Semi-streaming Maximization for k-Extendible Systems

## TL;DR

This paper introduces an almost optimal semi-streaming algorithm for maximizing weight under k-extendible constraints, significantly improving approximation ratios in the data stream model.

## Contribution

The paper presents a semi-streaming O(k log k)-approximation algorithm for the general k-extendible maximization problem, nearly matching offline bounds.

## Key findings

- Achieves near-optimal approximation ratio in semi-streaming model
- Improves upon previous algorithms with higher approximation factors
- Bridges gap between restricted and general cases

## Abstract

In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a semi-streaming $k^2(1 + \varepsilon)$-approximation algorithm (Crouch and Stubbs, 2014), but semi-streaming $O(k)$-approximation algorithms are known for many restricted cases of this general problem. In this paper, we close most of this gap by presenting a semi-streaming $O(k \log k)$-approximation algorithm for the general problem, which is almost the best possible even in the offline setting (Feldman et al., 2017).