Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online bin packing of squares and cubes   In the d-dimensional online bin packing problem, d-dimensional cubes of
positive sizes no larger than 1 are presented one by one to be assigned to
positions in d-dimensional unit cube bins. In this work, we provide improved
upper bounds on the asymptotic competitive ratio for square and cube bin
packing problems, where our bounds do not exceed 2.0885 and 2.5735 for square
and cube packing, respectively. To achieve these results, we adapt and improve
a previously designed harmonic-type algorithm, and apply a different method for
defining weight functions. We detect deficiencies in the state-of-the-art
results by providing counter-examples to the current best algorithms and the
analysis, where the claimed bounds were 2.1187 for square packing and 2.6161
for cube packing.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin