Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving and Sampling with Many Solutions: Satisfiability and Other Hard
  Problems   We investigate parameterizing hard combinatorial problems by the size of the
solution set compared to all solution candidates. Our main result is a uniform
sampling algorithm for satisfying assignments of 2-CNF formulas that runs in
expected time $O^*(\varepsilon^{-0.617})$ where $\varepsilon$ is the fraction
of assignments that are satisfying. This improves significantly over the
trivial sampling bound of expected $\Theta^*(\varepsilon^{-1})$, and on all
previous algorithms whenever $\varepsilon = \Omega(0.708^n)$. We also consider
algorithms for 3-SAT with an $\varepsilon$ fraction of satisfying assignments,
and prove that it can be solved in $O^*(\varepsilon^{-2.27})$ deterministic
time, and in $O^*(\varepsilon^{-0.936})$ randomized time. Finally, to further
demonstrate the applicability of this framework, we also explore how similar
techniques can be used for vertex cover problems.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph