Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Competitive Permutations for Set Cover by Intervals   We revisit the problem of computing an optimal partial cover of points by
intervals. We show that the greedy algorithm computes a permutation $\Pi =
\pi_1, \pi_2,\ldots$ of the intervals that is $3/4$-competitive for any prefix
of $k$ intervals. That is, for any $k$, the intervals $\pi_1 \cup \cdots \cup
\pi_k$ covers at least $3/4$-fraction of the points covered by the optimal
solution using $k$ intervals.
  We also provide an approximation algorithm that, in $O(n + m/\varepsilon)$
time, computes a cover by $(1+\varepsilon)k$ intervals that is as good as the
optimal solution using $k$ intervals, where $n$ is the number of input points,
and $m$ is the number of intervals (we assume here the input is presorted).
  Finally, we show a counter example illustrating that the optimal solutions
for set cover do not have the diminishing return property -- that is, the
marginal benefit from using more sets is not monotonically decreasing.
Fortunately, the diminishing returns does hold for intervals.

7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg