Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Truly Subcubic Min-Plus Product for Less Structured Matrices, with
  Applications   The goal of this paper is to get truly subcubic algorithms for Min-Plus
product for less structured inputs than what was previously known, and to apply
them to versions of All-Pairs Shortest Paths (APSP) and other problems. The
results are as follows:
  (1) Our main result is the first truly subcubic algorithm for the Min-Plus
product of two $n\times n$ matrices $A$ and $B$ with $\text{polylog}(n)$ bit
integer entries, where $B$ has a partitioning into $n^{\epsilon}\times
n^{\epsilon}$ blocks (for any $\epsilon>0$) where each block is at most
$n^\delta$-far (for $\delta<3-\omega$, where $2\leq \omega<2.373$) in
$\ell_\infty$ norm from a constant rank integer matrix. This result presents
the most general case to date of Min-Plus product that is solvable in truly
subcubic time.
  (2) The first application of our main result is a truly subcubic algorithm
for APSP in a new type of geometric graph. Our result extends the result of
Chan'10 in the case of integer edge weights by allowing the weights to differ
from a function of the end-point identities by at most $n^\delta$ for small
$\delta$.
  (3) In the second application we consider a batch version of the range mode
problem in which one is given a length $n$ sequence and $n$ contiguous
subsequences, and one is asked to compute the range mode of each subsequence.
We give the first $O(n^{1.5-\epsilon})$ time for $\epsilon>0$ algorithm for
this batch range mode problem.
  (4) Our final application is to the Maximum Subarray problem: given an
$n\times n$ integer matrix, find the contiguous subarray of maximum entry sum.
We show that Maximum Subarray can be solved in truly subcubic,
$O(n^{3-\epsilon})$ (for $\epsilon>0$) time, as long as the entries are no
larger than $O(n^{0.62})$ in absolute value.
  We also improve all the known conditional hardness results for the
$d$-dimensional variant of Maximum Subarray.

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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph