Elsevier

Theoretical Computer Science

Volume 412, Issue 39, 9 September 2011, Pages 5340-5350
Theoretical Computer Science

Approximating the longest paths in grid graphs

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Abstract

In this paper, we consider the problem of approximating the longest path in a grid graph that possesses a square-free 2-factor. By (1) analyzing several characteristics of four types of cross cells and (2) presenting three cycle-merging operations and one extension operation, we propose an algorithm that finds in an n-vertex grid graph G, a long path of length at least 56n+2. Our approximation algorithm runs in quadratic time. In addition to its theoretical value, our work has also an interesting application in image-guided maze generation.

Keywords

Long paths
Square-free 2-factor
Grid graphs

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