Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spines of Random Constraint Satisfaction Problems: Definition and
  Connection with Computational Complexity   We study the connection between the order of phase transitions in
combinatorial problems and the complexity of decision algorithms for such
problems. We rigorously show that, for a class of random constraint
satisfaction problems, a limited connection between the two phenomena indeed
exists. Specifically, we extend the definition of the spine order parameter of
Bollobas et al. to random constraint satisfaction problems, rigorously showing
that for such problems a discontinuity of the spine is associated with a
$2^{\Omega(n)}$ resolution complexity (and thus a $2^{\Omega(n)}$ complexity of
DPLL algorithms) on random instances. The two phenomena have a common
underlying cause: the emergence of ``large'' (linear size) minimally
unsatisfiable subformulas of a random formula at the satisfiability phase
transition.
  We present several further results that add weight to the intuition that
random constraint satisfaction problems with a sharp threshold and a continuous
spine are ``qualitatively similar to random 2-SAT''. Finally, we argue that it
is the spine rather than the backbone parameter whose continuity has
implications for the decision complexity of combinatorial problems, and we
provide experimental evidence that the two parameters can behave in a different
manner.

37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th