Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On-Line Partitioning of $d$-Dimensional Posets   An on-line chain partitioning algorithm receives a poset, one element at a
time, and irrevocably assigns the element to one of the chains. Over 30 years
ago, Szemer\'edi proved that any on-line algorithm could be forced to use
$\binom{w+1}{2}$ chains to partition a poset of width $w$. The maximum number
of chains that can be forced on any on-line algorithm remains unknown. In the
survey paper by Bosek, Felsner, Kloch, Krawczyk, Matecki and Micek, variants of
the original problem were studied where the class is restricted to
$d$-dimensional posets or where the poset is presented via a realizer of size
$d$. In this paper, we prove two results. First, we prove that any on-line
algorithm can be forced to use $(2-o(1))\binom{w+1}{2}$ chains to partition a
$2$-dimensional poset of width $w$. Second, we prove that any on-line algorithm
can be forced to use $(2-\frac{1}{d-1}-o(1))\binom{w+1}{2}$ chains to partition
a poset of width $w$ presented via a realizer of size $d$.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph