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arXiv · 1502.07085

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

Asghar Asgharian Sardroud·Alireza Bagheri
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Abstract

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.

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Asghar Asgharian Sardroud, Alireza Bagheri. 2015-02-25. An approximation algorithm for the longest cycle problem in solid grid graphs. https://arxiv.org/abs/1502.07085

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