计算路径和半包装
Counting Paths and Packings in Halves
摘要：
它表明，一个可以计数$k$ -边路径在$n$ -顶点图和$m$ -集$k$ -包装上的$n$ -元素的宇宙，分别在时间${n \choose k/2}$和${n \choose mk/2}$，直到一个因子多项式在$n$，$k$，和$m$ ;在多项式空间中，边界保持，如果乘以$3^{k/2}$或$5^{mk/2}$，分别。这些是一个更一般的结果的含义：给定$n$ -元素论域上的两个集合族，人们可以用$\nO(n \ell)$基本运算来计算两个集合族的笛卡尔积中的不相交集合对，其中$\ell$是两个集合族及其子集中的成员数。
英文摘要：
It is shown that one can count $k$-edge paths in an $n$-vertex graph and $m$-set $k$-packings on an $n$-element universe, respectively, in time ${n \choose k/2}$ and ${n \choose mk/2}$, up to a factor polynomial in $n$, $k$, and $m$; in polynomial space, the bounds hold if multiplied by $3^{k/2}$ or $5^{mk/2}$, respectively. These are implications of a more general result: given two set families on an $n$-element universe, one can count the disjoint pairs of sets in the Cartesian product of the two families with $\nO(n \ell)$ basic operations, where $\ell$ is the number of members in the two families and their subsets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
