Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum
  Chain Covers in Convex Bipartite Graphs   A bipartite graph $G=(U,V,E)$ is convex if the vertices in $V$ can be
linearly ordered such that for each vertex $u\in U$, the neighbors of $u$ are
consecutive in the ordering of $V$. An induced matching $H$ of $G$ is a
matching such that no edge of $E$ connects endpoints of two different edges of
$H$. We show that in a convex bipartite graph with $n$ vertices and $m$
weighted edges, an induced matching of maximum total weight can be computed in
$O(n+m)$ time. An unweighted convex bipartite graph has a representation of
size $O(n)$ that records for each vertex $u\in U$ the first and last neighbor
in the ordering of $V$. Given such a compact representation, we compute an
induced matching of maximum cardinality in $O(n)$ time.
  In convex bipartite graphs, maximum-cardinality induced matchings are dual to
minimum chain covers. A chain cover is a covering of the edge set by chain
subgraphs, that is, subgraphs that do not contain induced matchings of more
than one edge. Given a compact representation, we compute a representation of a
minimum chain cover in $O(n)$ time. If no compact representation is given, the
cover can be computed in $O(n+m)$ time.
  All of our algorithms achieve optimal running time for the respective problem
and model. Previous algorithms considered only the unweighted case, and the
best algorithm for computing a maximum-cardinality induced matching or a
minimum chain cover in a convex bipartite graph had a running time of $O(n^2)$.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga