Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contiguous Cake Cutting: Hardness Results and Approximation Algorithms   We study the fair allocation of a cake, which serves as a metaphor for a
divisible resource, under the requirement that each agent should receive a
contiguous piece of the cake. While it is known that no finite envy-free
algorithm exists in this setting, we exhibit efficient algorithms that produce
allocations with low envy among the agents. We then establish NP-hardness
results for various decision problems on the existence of envy-free
allocations, such as when we fix the ordering of the agents or constrain the
positions of certain cuts. In addition, we consider a discretized setting where
indivisible items lie on a line and show a number of hardness results extending
and strengthening those from prior work. Finally, we investigate connections
between approximate and exact envy-freeness, as well as between continuous and
discrete cake cutting.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th