Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Max-Sum Diversification, Monotone Submodular Functions and Semi-metric
  Spaces   In many applications such as web-based search, document summarization,
facility location and other applications, the results are preferable to be both
representative and diversified subsets of documents. The goal of this study is
to select a good "quality", bounded-size subset of a given set of items, while
maintaining their diversity relative to a semi-metric distance function. This
problem was first studied by Borodin et al\cite{borodin}, but a crucial
property used throughout their proof is the triangle inequality. In this
modified proof, we want to relax the triangle inequality and relate the
approximation ratio of max-sum diversification problem to the parameter of the
relaxed triangle inequality in the normal form of the problem (i.e., a uniform
matroid) and also in an arbitrary matroid.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ