Fair Rent Division: New Budget and Rent Constraints
Rohith Reddy Gangam, Shayan Taherijam, Vijay V. Vazirani
TL;DR
The paper tackles envy-free rent division with indivisible rooms under two realistic constraints: per-room rent bounds and agent-specific budgets for each room. It develops a suite of combinatorial, strongly polynomial-time algorithms built around envy graphs and strongly connected components to compute EF allocations or certify infeasibility, while also optimizing EF outcomes under maximin, leximin, and minimum-spread criteria. A unifying framework is presented that can handle either constraint type individually and in combination, enabling scalable, fair allocations suitable for real platforms like Spliddit. The work advances practical fair division by embracing realistic financial and contractual constraints without sacrificing the guarantees of envy-freeness or computational efficiency.
Abstract
We study the classical rent division problem, where $n$ agents must allocate $n$ indivisible rooms and split a fixed total rent $R$. The goal is to compute an envy-free (EF) allocation, where no agent prefers another agent's room and rent to their own. This problem has been extensively studied under standard assumptions, where efficient algorithms for computing EF allocations are known. We extend this framework by introducing two practically motivated constraints: (i) lower and upper bounds on room rents, and (ii) room-specific budget for agents. We develop efficient combinatorial algorithms that either compute a feasible EF allocation or certify infeasibility. We further design algorithms to optimize over EF allocations using natural fairness objectives such as maximin utility, leximin utility, and minimum utility spread. Our approach unifies both constraint types within a single algorithmic framework, advancing the applicability of fair division methods in real-world platforms such as Spliddit.