An approximation algorithm for the longest cycle problem in solid grid graphs

摘要

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 2n/3 + 1 in 2-connected n-node solid grid graphs. (C) 2015 Elsevier B.V. All rights reserved.