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

All || By Area || By YearTitle | Snakes, coils, and single-track circuit codes with spread k |
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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 |

Link | |

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. |

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