Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum 0-1 Timed Matching on Temporal Graphs   Temporal graphs are graphs where the topology and/or other properties of the
graph change with time. They have been used to model applications with temporal
information in various domains. Problems on static graphs become more
challenging to solve in temporal graphs because of dynamically changing
topology, and many recent works have explored graph problems on temporal
graphs. In this paper, we define a type of matching called {\em 0-1 timed
matching} for temporal graphs, and investigate the problem of finding a {\em
maximum 0-1 timed matching} for different classes of temporal graphs. We first
prove that the problem is NP-Complete for rooted temporal trees when each edge
is associated with two or more time intervals. We then propose an $O(n \log n)$
time algorithm for the problem on a rooted temporal tree with $n$ nodes when
each edge is associated with exactly one time interval. The problem is then
shown to be NP-Complete also for bipartite temporal graphs even when each edge
is associated with a single time interval and degree of each node is bounded by
a constant $k \geq 3$. We next investigate approximation algorithms for the
problem for temporal graphs where each edge is associated with more than one
time intervals. It is first shown that there is no
$\frac{1}{n^{1-\epsilon}}$-factor approximation algorithm for the problem for
any $\epsilon > 0$ even on a rooted temporal tree with $n$ nodes unless NP =
ZPP. We then present a $\frac{5}{2\mathcal{N}^* + 3}$-factor approximation
algorithm for the problem for general temporal graphs where $\mathcal{N^*}$ is
the average number of edges overlapping in time with each edge in the temporal
graph. The same algorithm is also a constant-factor approximation algorithm for
degree bounded temporal graphs.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph