Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifying Homology Classes   We develop a method for measuring homology classes. This involves three
problems. First, we define the size of a homology class, using ideas from
relative homology. Second, we define an optimal basis of a homology group to be
the basis whose elements' size have the minimal sum. We provide a greedy
algorithm to compute the optimal basis and measure classes in it. The algorithm
runs in $O(\beta^4 n^3 \log^2 n)$ time, where $n$ is the size of the simplicial
complex and $\beta$ is the Betti number of the homology group. Third, we
discuss different ways of localizing homology classes and prove some hardness
results.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph