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Finding Longest Paths in Hypercubes: 11 New Lower Bounds for Snakes, Coils, and Symmetrical Coils

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Current Approaches in Applied Artificial Intelligence (IEA/AIE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9101))

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Abstract

Since the problem’s formulation by Kautz in 1958 as an error detection tool, diverse applications for long snakes and coils have been found. These include coding theory, electrical engineering, and genetics. Over the years, the problem has been explored by many researchers in different fields using varied approaches, and has taken on additional meaning. The problem has become a benchmark for evaluating search techniques in combinatorially expansive search spaces (NP-complete Optimizations).

We build on our previous work and present improved heuristics for Stochastic Beam Search sub-solution selection in searching for longest induced paths: open (snakes), closed (coils), and symmetric closed (symmetric coils); in n-dimensional hypercube graphs. Stochastic Beam Search, a non-deterministic variant of Beam Search, provides the overall structure for our search. We present eleven new lower bounds for the Snake-in-the-Box problem for snakes in dimensions 11, 12, and 13; coils in dimensions 10, 11, and 12; and symmetric coils in dimensions 9, 10, 11, 12, and 13. The best known solutions of the unsolved dimensions of this problem have improved over the years and we are proud to make a contribution to this problem as well as the continued progress in combinatorial search techniques.

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Authors and Affiliations

  1. Computer Science Department, University of Georgia, Athens, USA

    Seth J. Meyerson, William E. Whiteside & Walter D. Potter

  2. Institute for Artificial Intelligence, University of Georgia, Athens, Georgia, USA

    Thomas E. Drapela & Walter D. Potter

Authors
  1. Seth J. Meyerson
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  2. Thomas E. Drapela
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  3. William E. Whiteside
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  4. Walter D. Potter
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Corresponding author

Correspondence to Seth J. Meyerson .

Editor information

Editors and Affiliations

  1. Texas State University, San Marcos, Texas, USA

    Moonis Ali

  2. Dongguk University, Seoul, Korea, Republic of (South Korea)

    Young Sig Kwon

  3. Dongguk University, Seoul, Korea, Republic of (South Korea)

    Chang-Hwan Lee

  4. Dongguk University, Seoul, Korea, Republic of (South Korea)

    Juntae Kim

  5. Seoul National University, Seoul, Korea, Republic of (South Korea)

    Yongdai Kim

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Meyerson, S.J., Drapela, T.E., Whiteside, W.E., Potter, W.D. (2015). Finding Longest Paths in Hypercubes: 11 New Lower Bounds for Snakes, Coils, and Symmetrical Coils. In: Ali, M., Kwon, Y., Lee, CH., Kim, J., Kim, Y. (eds) Current Approaches in Applied Artificial Intelligence. IEA/AIE 2015. Lecture Notes in Computer Science(), vol 9101. Springer, Cham. https://doi.org/10.1007/978-3-319-19066-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-19066-2_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19065-5

  • Online ISBN: 978-3-319-19066-2

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