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Cake cutting research tackles proportional allocation complexity · 2 papers

By PulseAugur Editorial · [3 sources] ·

Two new research papers explore the complexities of proportional cake cutting, a theoretical problem in multiagent systems. The first paper determines the exact worst-case number of cuts needed to guarantee an equal-length proportional allocation, improving on previous bounds and discussing computational feasibility. The second paper proves that computing a contiguous envy-free cake allocation is PPAD-complete, even under simplified valuation conditions, highlighting the computational difficulty of such problems. AI

IMPACT These papers explore theoretical underpinnings of fair resource allocation, relevant to multi-agent AI systems.

RANK_REASON Two academic papers published on arXiv concerning theoretical computer science problems.

Read on arXiv cs.MA (Multiagent) →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

Cake cutting research tackles proportional allocation complexity · 2 papers

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COVERAGE [3]

  1. arXiv cs.MA (Multiagent) TIER_1 English(EN) · Mohammad Azharuddin Sanpui ·

    Exact Cut Complexity of Equal-Length Proportional Cake Cutting

    We study proportional cake cutting under an equal-length constraint, where each of $n$ agents must receive a bundle of length exactly $1/n$ that is worth at least $1/n$ to that agent. Our main result determines the exact worst-case number of cuts needed to guarantee such an alloc…

  2. arXiv cs.MA (Multiagent) TIER_1 English(EN) · Mohammad Azharuddin Sanpui ·

    PPAD-Completeness of Contiguous Envy-Free Cake Cutting with Additive Valuations

    We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\varepsilon$ is given in unary, and even when every density takes only two values, …

  3. Hugging Face Daily Papers TIER_1 English(EN) ·

    PPAD-Completeness of Contiguous Envy-Free Cake Cutting with Additive Valuations

    We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\varepsilon$ is given in unary, and even when every density takes only two values, …

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