Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.02724

Almost Envy-Freeness for Additive Mixed Manna with Entitlements: Deterministic and Randomized Guarantees

Zehan Lin·Shengxin Liu·Biaoshuai Tao·Shengwei Zhou
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the fair allocation of indivisible items among agents with asymmetric entitlements in mixed manna settings, where the items consist of both goods and chores. For additive valuations, we establish that weighted envy-free up to one item (WEF1) allocations always exist and can be computed in polynomial time. We also study fair and efficient allocation and show that weighted envy-freeness up to one transfer (WEF1T) is compatible with fractional Pareto optimality (fPO) for every mixed-manna instance. This relaxation from WEF1 to WEF1T is tight, as demonstrated by our impossibility result. We further show a best-of-both-worlds result via a finite lottery that guarantees weighted envy-freeness (WEF) in expectation, with every realized allocation satisfying WEF1T and achieving the tight characterization complemented by the existing impossibility result.

Explore related subjects

cs.GT

Keep this discovery

BibTeXRIS

Zehan Lin, Shengxin Liu, Biaoshuai Tao, Shengwei Zhou. 2026-09-02. Almost Envy-Freeness for Additive Mixed Manna with Entitlements: Deterministic and Randomized Guarantees. https://arxiv.org/abs/2609.02724

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.GT subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

arXiv2026

Self-Geometry: GT-Free and Plug-and-Play Test-Time Adaptation for Geometrically Consistent 3D Vision Foundation Models

Recent Vision Foundation Models (VFMs) predict depth, camera pose, and pointmap in a single forward pass without per-scene optimization, achieving strong generalization. However, enforcing explicit multi-view geometric consistency, e.g., through bundle adjustment, is computationally costly and is thus not imposed during VFM pretraining, so such inconsistency can arise. To address this, implicit self-consistency derived from model outputs (e.g., pointmaps, features), though enforced at test-time in prior work, delivers inherently limited performance gain, especially on scenes where the pretrained VFM is highly inaccurate. In contrast to this implicit signal, we propose Self-Geometry, a plug-and-play test-time adaptation pipeline that directly imposes explicit multi-view geometric constraints using 2D pixel correspondences as pseudo ground-truth. Our proposed Self-Geometry consists of Geometric Disentanglement Optimization, which combines Multi-View Consistency and Epipolar Consistency losses with Gradient Disentanglement to prevent gradient conflict; Frame Angular-Neighbor, a view sampler based on SO(3) geodesic distances for lightly imposing these constraints; and Lightweight TTA, which adapts VFMs via LoRA. Our method achieves consistent improvements in both pose and geometry estimation across six VFMs (VGGT, $π^3$, DA3-Giant/Large/Base/Small) and four benchmarks (7Scenes, ETH3D, ScanNet++, HiRoom).

cs.CV↗
arXiv2026

Jointly Satisfying Pareto Optimality and Justified Representation is NP-Hard in Approval-Based Multiwinner Voting

An open problem in approval-based multiwinner voting concerns whether we can efficiently compute committees that satisfy both justified representation and Pareto optimality. We answer this question negatively by proving that, on the domain of all profiles, outputting a committee satisfying both axioms is NP-hard. An initial proof was found by ChatGPT Astra. This was then verified and rewritten by the author.

cs.GT↗