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Research Paper#Graph Theory, Parameterized Complexity, Fair Division🔬 ResearchAnalyzed: Jan 3, 2026 06:13

Parameterized Complexity of Fair Orientations in Graphs

Published:Dec 31, 2025 18:30
1 min read
ArXiv

Analysis

This paper investigates the computational complexity of finding fair orientations in graphs, a problem relevant to fair division scenarios. It focuses on EF (envy-free) orientations, which have been less studied than EFX orientations. The paper's significance lies in its parameterized complexity analysis, identifying tractable cases, hardness results, and parameterizations for both simple graphs and multigraphs. It also provides insights into the relationship between EF and EFX orientations, answering an open question and improving upon existing work. The study of charity in the orientation setting further extends the paper's contribution.
Reference

“The paper initiates the study of EF orientations, mostly under the lens of parameterized complexity, presenting various tractable cases, hardness results, and parameterizations.”

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AI Research#Fair Division, Resource Allocation, Distributed Systems🔬 ResearchAnalyzed: Jan 4, 2026 06:51

Beyond Exact Fairness: Envy-Free Incomplete Connected Fair Division

Published:Dec 27, 2025 05:38
1 min read
ArXiv

Analysis

This paper explores fair division in scenarios where complete connectivity isn't possible, introducing the concept of 'envy-free' division in incomplete connected settings. The research likely delves into the challenges of allocating resources or items fairly when not all parties can interact directly, a common issue in distributed systems or network resource allocation. The paper's contribution lies in extending fairness concepts to more realistic, less-connected environments.
Reference

“The paper likely provides algorithms or theoretical frameworks for achieving envy-free division under incomplete connectivity constraints.”

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