Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An O(M log M) Algorithm for Bipartite Matching with Roadmap Distances   An algorithm is presented which produces the minimum cost bipartite matching
between two sets of M points each, where the cost of matching two points is
proportional to the minimum distance by which a particle could reach one point
from the other while constrained to travel on a connected set of curves, or
roads. Given any such roadmap, the algorithm obtains O(M log M) total runtime
in terms of M, which is the best possible bound in the sense that any algorithm
for minimal matching has runtime Omega(M log M). The algorithm is strongly
polynomial and is based on a capacity-scaling approach to the [minimum] convex
cost flow problem. The result generalizes the known Theta(M log M) complexity
of computing optimal matchings between two sets of points on (i) a line
segment, and (ii) a circle.

32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics