arXiv subjects

Noga Klein Elmalem

Publications and source records attributed to Noga Klein Elmalem.

5 recordsLinked to original sources

arXiv2026

The Min Max Average Cycle Weight Problem

When an old apartment building is demolished and rebuilt, how can we fairly redistribute the new apartments to minimize envy among residents? We reduce this question to a combinatorial optimization problem called the *Min Max Average Cycle Weight* problem. In that problem we seek to assign objects to agents in a way that minimizes the maximum average weight of directed cycles in an associated envy graph. While this problem reduces to maximum-weight matching when starting from a clean slate (achieving polynomial-time solvability), we show that this is not the case when we account for preexisting conditions, such as residents' satisfaction with their original apartments. Whether the problem is polynomial-time solvable in the general case remains an intriguing open problem.

cs.DS↗

arXiv2026

Fair Allocation of Improvements: When Old Endowments Shape New Assignments

This work is motivated by a common urban renewal process called Reconstruct and Divide. It involves the demolition of old buildings and the construction of new ones. Original homeowners are compensated with upgraded apartments, while surplus units are sold for profit, so theoretically it is a win-win project for all parties involved. However, many Reconstruct and Divide projects are withheld or delayed due to disagreements over the assignment of new apartments, claiming they are not fair. The goal of this research is to develop algorithms for envy-free assignment of the new apartments, possibly using monetary payments to reduce envy. In contrast to previous works on envy-free assignment, in our setting the envy depends also on the value of the old apartments, as people with more valuable old apartments expect to get more valuable new apartments. This presents two challenges. First, in some cases, no assignment and payment-vector satisfy the common fairness notions of envy-freeness and proportionality. Hence, we focus on minimizing the envy and the disproportionality (the distance between an agent's value and their proportional share). We present a strongly polynomial-time algorithm that, for a given assignment, finds a payment vector that minimizes the maximum pairwise-envy. We also present a strongly polynomial-time algorithm that computes an assignment and payment-vector that together minimize the maximum disproportionality. Second, directly asking the agents for their subjective valuations for their old apartments is infeasible, as it is a dominant strategy for them to report very high values for their old apartments. We introduce a novel method to elicit agents' valuations indirectly. Using this method, we identify conditions under which our Minimum Disproportionality algorithm is risk-averse truthful.

cs.GT↗

arXiv2025

Fair Allocation with Money: What is Your Objective?

When allocating indivisible items, there are various ways to use monetary transfers for eliminating envy. Particularly, one can apply a balanced vector of transfer payments, or charge each agent a positive amount, or -- contrarily -- give each agent a positive amount as a ``subsidy''. In each model, one can aim to minimize the amount of payments used; this aim translates into different optimization objectives in each setting. This note compares the various models, and the relations between upper and lower bounds for these objectives.

cs.GT↗

arXiv2025

Whoever Said Money Won't Solve All Your Problems? Weighted Envy-free Allocation with Subsidy

We explore solutions for fairly allocating indivisible items among agents assigned weights representing their entitlements. Our fairness goal is weighted-envy-freeness (WEF), where each agent deems their allocated portion relative to their entitlement at least as favorable as any others relative to their own. Often, achieving WEF necessitates monetary transfers, which can be modeled as third-party subsidies. The goal is to attain WEF with bounded subsidies. Previous work relied on characterizations of unweighted envy-freeness (EF), that fail in the weighted setting. This makes our new setting challenging. We present polynomial-time algorithms that compute WEF allocations with a guaranteed upper bound on total subsidy for monotone valuations and various subclasses thereof. We also present an efficient algorithm to compute a fair allocation of items and money, when the budget is not enough to make the allocation WEF. This algorithm is new even for the unweighted setting.

cs.GT↗

arXiv2025

Weighted Envy Freeness With Bounded Subsidies

We explore solutions for fairly allocating indivisible items among agents assigned weights representing their entitlements. Our fairness goal is weighted-envy-freeness (WEF), where each agent deems their allocated portion relative to their entitlement at least as favorable as any other's relative to their own. In many cases, achieving WEF necessitates monetary transfers, which can be modeled as third-party subsidies. The goal is to attain WEF with bounded subsidies. Previous work in the unweighted setting of subsidies relied on basic characterizations of EF that fail in the weighted settings. This makes our new setting challenging and theoretically intriguing. We present polynomial-time algorithms that compute WEF-able allocations with an upper bound on the subsidy per agent in three distinct additive valuation scenarios: (1) general, (2) identical, and (3) binary. When all weights are equal, our bounds reduce to the bounds derived in the literature for the unweighted setting.

cs.GT↗