Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Approximation Performance of Degree Heuristics for Matching   In the design of greedy algorithms for the maximum cardinality matching
problem the utilization of degree information when selecting the next edge is a
well established and successful approach.
  We define the class of "degree sensitive" greedy matching algorithms, which
allows us to analyze many well-known heuristics, and provide tight
approximation guarantees under worst case tie breaking. We exhibit algorithms
in this class with optimal approximation guarantee for bipartite graphs. In
particular the Karp-Sipser algorithm, which picks an edge incident with a
degree-1 node if possible and otherwise an arbitrary edge, turns out to be
optimal with approximation guarantee D/(2D-2), where D is the maximum degree.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin