Hana Salavcová – DIMACS REU Summer 2025

Week 1

• Read introductory materials on fair allocation problems
• Initial meeting with mentor to discuss basics of fair allocation and possible research directions
• Brainstormed new research idea and discussed possible settings and models with Martin to formalize the approach
• Began outlining ideas for the initial presentation

Literature

• Amanatidis et al. (2023). Fair division of indivisible goods: Recent progress and open questions. [DOI]
• Aziz et al. (2022). Algorithmic fair allocation of indivisible items: A survey and new questions. [DOI]

Week 2

• Finished preparing the initial presentation
• Shared our Overleaf document and initial notes with our mentor
• Held a short online meeting to discuss early ideas and feedback
• Presented our initial presentation [view slides]
• Significantly rewrote and reorganized our notes describing the shared setting (now with formal definitions and clearer structure)
• Added basic proofs of fundamental properties of the model
• Had an extended in-person meeting with our mentor to discuss various possible fairness notions (e.g., multiple variants of EFX, MMS)
• Noted a connection between MMS in the cost-free setting and MMS in constrained settings

Literature

• Kurokawa, Procaccia, and Wang (2018). Fair Enough: Guaranteeing Approximate Maximin Shares. [DOI]
• Anonymous (n.d.). Preprint manuscript, details withheld for confidentiality.
• Chaudhury et al. (2021). A Little Charity Guarantees Almost Envy-Freeness. [DOI]

Week 3

• Updated the Overleaf template to make collaborative editing more structured and readable
• Added new existential results for MMS and a preliminary result for EFX (which later turned out to be incorrect :( )
• Attended the Tuesday seminar on mechanism design (mostly introductory, but engaging!)
• Established a result connecting EFX across goods and chores
• Met with our mentor on Thursday and agreed on formalization of the model and fairness notions
• Reviewed and discussed our results related to SMMS and MMS — mentor was pleasantly surprised by our progress
• Received detailed feedback on our Overleaf document (notation and further directions) and alredy addressed part of the comments and planned to revisit a specific result next week
• Made initial progress on PROPx-related results
• Participated in Friday's Culture Day, presented a Czech animal sound quiz (e.g., “chro chro”), enjoyed presentations and food!

Literature

• Feige, Sapir, and Tauber (2021). A tight negative example for MMS fair allocations. [DOI]
• Guo et al. (2023). A Survey on Fair Allocation of Chores. [DOI]

Week 4

Literature

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