Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Equivalence among Problems of Bounded Width   In this paper, we introduce a methodology, called decomposition-based
reductions, for showing the equivalence among various problems of
bounded-width.
  First, we show that the following are equivalent for any $\alpha > 0$:
  * SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time,
  * 3-SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time,
  * Max 2-SAT can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time,
  * Independent Set can be solved in $O^*(2^{\alpha \mathrm{tw}})$ time, and
  * Independent Set can be solved in $O^*(2^{\alpha \mathrm{cw}})$ time, where
tw and cw are the tree-width and clique-width of the instance, respectively.
  Then, we introduce a new parameterized complexity class EPNL, which includes
Set Cover and Directed Hamiltonicity, and show that SAT, 3-SAT, Max 2-SAT, and
Independent Set parameterized by path-width are EPNL-complete. This implies
that if one of these EPNL-complete problems can be solved in $O^*(c^k)$ time,
then any problem in EPNL can be solved in $O^*(c^k)$ time.

27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ