  Although, the Hamiltonicity of solid grid graphs are polynomial-time
decidable, the complexity of the longest cycle problem in these graphs is still
open. In this paper, by presenting a linear-time constant-factor approximation
algorithm, we show that the longest cycle problem in solid grid graphs is in
APX. More precisely, our algorithm finds a cycle of length at least
$\frac{2n}{3}+1$ in 2-connected $n$-node solid grid graphs.
  Keywords: Longest cycle, Hamiltonian cycle, Approximation algorithm, Solid
grid graph.
