论文标题
最佳周期包含$ k $ dimensional hypercube的所有节点
Optimal cycles enclosing all the nodes of a $k$-dimensional hypercube
论文作者
论文摘要
我们通过使用具有最小链接的多边形链来访问$ k $二维超模的所有$ 2^k $节点的总体问题，我们表明此最佳值由$ h（2，k）给出：= 3 \ cdot 2^{k-2^{k-2} $ if and if $ k \ in \ in \ in \ nath \ n n \ n n \ n} $ n} $} 0,000,1-0.此外，对于上一个上述所有上述节点，$ h（2，k）：= \ {\ {0,1 \} \} \ times \ {0,1 \} \ times \ times \ dips \ dips \ dips \ {0,11 \ {0,11 \} \ \ Mathbb {r}^k $，具有一个周期（即封闭路径），只有$ 3 \ cdot 2^{k-2} $链接。
We solve the general problem of visiting all the $2^k$ nodes of a $k$-dimensional hypercube by using a polygonal chain that has minimum link-length, and we show that this optimal value is given by $h(2,k):=3 \cdot 2^{k-2}$ if and only if $k \in \mathbb{N}-\{0,1\}$. Furthermore, for any $k$ above one, we constructively prove that it is possible to visit once and only once all the aforementioned nodes, $H(2,k):=\{\{0,1\} \times \{0,1\} \times \dots \times \{0,1\}\} \subset \mathbb{R}^k$, with a cycle (i.e., a closed path) having only $3 \cdot 2^{k-2}$ links.
