Publication: Snakes, coils, and single-track circuit codes with spread k

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Title	Snakes, coils, and single-track circuit codes with spread k
Authors/Editors*	Simon Hood, Daniel Recoskie, Joe Sawada, Dennis Wong
Where published*	Journal of Combinatorial Optimization
How published*	Journal
Year*	2013
Volume
Number
Pages	21
Publisher	Springer
Keywords	Snake, Coil, Circuit code, Single-track, Snake-in-the-box, Longest path
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Abstract	The snake-in-the-box problem is concerned with finding a longest induced path in a hypercube Q_n. Similarly, the coil-in-the-box problem is concerned with finding a longest induced cycle in Q_n.We consider a generalization of these problems that considers paths and cycles where each pair of vertices at distance at least k in the path or cycle are also at distance at least k in Q_n. We call these paths k-snakes and the cycles k-coils. The k-coils have also been called circuit codes. By optimizing an exhaustive search algorithm, we find 13 new longest k-coils, 21 new longest k-snakes and verify that some of them are optimal. By optimizing an algorithm by Paterson and Tuliani to find single-track circuit codes, we additionally find another 8 new longest k-coils. Using these k-coils with some basic backtracking, we find 18 new longest k-snakes.