Envy minimization¶

In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible.

Version: v1 · 2026-09-28 · History
Domain-specific #: 9272
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Subdomains: Algorithmic Game Theory, Fair Division → Computer Science & Software Engineering

Core Idea¶

Envy minimization is treated here as the recurring mathematicslogicstatistics identity summarized by this source-grounded definition: In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible. In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible.

Scope of Application¶

Defining the amount of envy. There are several ways to define the objective function (the amount of envy) for minimization.
Online minimization of the envy-difference. An example application is the problem of a food bank, which accepts food donations and must allocate them immediately to charities.
Online minimization of the envy-difference. The reduction has been used to obtain bounds for minimizing the envy-difference in various works including Jiang, Kulkarni, and Singla.
Documented setting. One approach for coping with this impossibility is to turn the problem to an optimization problem, in which the loss function is a function describing the amount of envy.
Documented setting. However, there are optimization algorithms that can yield good results in practice.

Clarity¶

A clear use of Envy minimization names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible.

Manages Complexity¶

Envy minimization compresses multiple mathematicslogicstatistics details into a stable diagnostic relation. The source shows both the central mechanism—this problem can be solved by presenting it as an Asymmetric distributed constraint optimization problem (ADCOP) as follows.—and the practical consequence—the following greedy algorithm finds an allocation whose maximum envy-ratio is at most 1.4 times the optimum.

Abstract Reasoning¶

Type the carrier. Identify the mathematicslogicstatistics entities to which the claim applies.
State the relation. Use the source-grounded identity: In computer science and operations research, the envy minimization problem is the problem of allocating discrete items among agents with different valuations over the items, such that the amount of envy is as small as possible.
Check operation and conditions. All agents are ordered lexicographically (e.g. by their name or index).
Demand recognition evidence. The variable is owned by agent i.
Test variation.

Knowledge Transfer¶

Within the home domain. Knowledge about Envy minimization transfers literally when a new case preserves the same carrier type, relation, and recognition test. There are several ways to define the objective function (the amount of envy) for minimization. An example application is the problem of a food bank, which accepts food donations and must allocate them immediately to charities. Beyond the home domain. No canonical parent is asserted for Envy minimization.

Relationships to Other Abstractions¶

Current abstraction Envy minimization Domain-specific

Parents (1) — more general patterns this builds on

Envy minimization is a kind of Computational problem Domain-specific

Envy minimization specifies encoded allocation instances, feasible allocations, and the objective of minimizing declared envy.

Hierarchy path (1) — routes to 1 parentless root

Envy minimization → Computational problem → Function (Mapping)

Neighborhood in Abstraction Space¶

Envy minimization sits in a sparse region of the domain-specific corpus (61^st percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08