Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardness of Vertex Deletion and Project Scheduling   Assuming the Unique Games Conjecture, we show strong inapproximability
results for two natural vertex deletion problems on directed graphs: for any
integer $k\geq 2$ and arbitrary small $\epsilon > 0$, the Feedback Vertex Set
problem and the DAG Vertex Deletion problem are inapproximable within a factor
$k-\epsilon$ even on graphs where the vertices can be almost partitioned into
$k$ solutions. This gives a more structured and therefore stronger UGC-based
hardness result for the Feedback Vertex Set problem that is also simpler
(albeit using the "It Ain't Over Till It's Over" theorem) than the previous
hardness result.
  In comparison to the classical Feedback Vertex Set problem, the DAG Vertex
Deletion problem has received little attention and, although we think it is a
natural and interesting problem, the main motivation for our inapproximability
result stems from its relationship with the classical Discrete Time-Cost
Tradeoff Problem. More specifically, our results imply that the deadline
version is NP-hard to approximate within any constant assuming the Unique Games
Conjecture. This explains the difficulty in obtaining good approximation
algorithms for that problem and further motivates previous alternative
approaches such as bicriteria approximations.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex