Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a weighted linear matroid intersection algorithm by deg-det
  computation   In this paper, we address the weighted linear matroid intersection problem
from the computation of the degree of the determinants of a symbolic matrix. We
show that a generic algorithm computing the degree of noncommutative
determinants, proposed by the second author, becomes an $O(mn^3 \log n)$ time
algorithm for the weighted linear matroid intersection problem, where two
matroids are given by column vectors $n \times m$ matrices $A,B$. We reveal
that our algorithm is viewed as a "nonstandard" implementation of Frank's
weight splitting algorithm for linear matroids. This gives a linear algebraic
reasoning to Frank's algorithm. Although our algorithm is slower than existing
algorithms in the worst case estimate, it has a notable feature: Contrary to
existing algorithms, our algorithm works on different matroids represented by
another "sparse" matrices $A^0,B^0$, which skips unnecessary Gaussian
eliminations for constructing residual graphs.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-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
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th