Lower Bound for Online MMS Assignment of Indivisible Chores

TL;DR

This paper proves a new lower bound of n on the competitive ratio for deterministic online algorithms assigning indivisible chores among n agents, improving previous bounds and highlighting fundamental limitations.

Contribution

It establishes a tighter lower bound of n for the competitive ratio in online chore assignment, advancing understanding of algorithmic limitations.

Findings

No deterministic online algorithm can achieve a competitive ratio better than n.

The lower bound applies to any number of agents n.

This result improves upon the previous bound of 2.

Abstract

We consider the problem of online assignment of indivisible chores under \MMS\ criteria. The previous work proves that any deterministic online algorithm for chore division has a competitive ratio of at least 2. In this work, we improve this bound by showing that no deterministic online algorithm can obtain a competitive ratio better than $n$ for $n$ agents.