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The DNA of Snakes

机译：蛇的DNA

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摘要

The Snake in the Box problem is an NP-Hard problem. The goal is to find the longest maximal snakes (a certain kind of path satisfying particular constraints described as "spread") in an n-dimensional hypercube. With increasing dimensions the search space grows exponentially and the search for snakes becomes more and more difficult. This article identifies an underlying pattern among the known longest snakes in previously searched dimensions, which resembles the DNA of living cells in many ways. Surprisingly, these generic structures are fundamentally different for the four combinations of odd and even dimension and spread It briefly explains the reason why they have different underlying structures. In odd dimensions with odd spread, there is one symmetric point and a unique mapping of complementary transition pairs and are discussed in detail in this paper. This article focusses only on one of these - odd dimension with odd spread. Later, it also reports three new lower bounds that are established using these generic structures from previously known longest maximal snakes. Another known longest snake in another odd dimension with odd spread is also found using this approach.
机译：盒中蛇问题是NP-Hard问题。目标是在n维超立方体中找到最长的最大蛇（满足特定约束条件的某种路径，称为“传播”）。随着尺寸的增加，搜索空间呈指数增长，并且对蛇的搜索变得越来越困难。本文确定了先前搜索到的已知最长蛇中的潜在模式，该模式在许多方面类似于活细胞的DNA。令人惊讶的是，这些通用结构对于奇数和偶数维以及价差的四个组合根本不同。它简要说明了它们具有不同基础结构的原因。在具有奇数展布的奇数维中，存在一个对称点和互补过渡对的唯一映射，本文将对此进行详细讨论。本文仅关注其中之一-具有奇数传播的奇数维。后来，它还报告了三个新的下界，这些下界是使用这些已知的最长的最大蛇的通用结构建立的。使用这种方法还发现了另一个已知的最长蛇，它在另一个奇数维中具有奇数传播。

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