We show an $O(n)$-time reduction from the problem of testing whether a multiset of positive integers can be partitioned into two multisets so that the sum of the integers in each multiset is equal to $n/2$ to the problem of testing whether an $n$-vertex biconnected outerplanar DAG admits an upward planar drawing. This constitutes the first barrier to the existence of efficient algorithms for testing the upward planarity of DAGs with no large triconnected minor. We also show a result in the opposite direction. Suppose that partitioning a multiset of positive integers into two multisets so that the sum of the integers in each multiset is $n/2$ can be solved in $f(n)$ time. Let $G$ be an $n$-vertex biconnected outerplanar DAG and $e$ be an edge incident to the outer face of an outerplanar drawing of $G$. Then it can be tested in $O(f(n))$ time whether $G$ admits an upward planar drawing with $e$ on the outer face.

翻译：我们展示了一个从判断正整数多重集是否能划分为两个和均为$n/2$的多重集的问题，到判断$n$顶点双连通外平面有向无环图是否允许向上平面画图的问题的$O(n)$时间归约。这一结果构成了在无大三连通子式情况下，测试有向无环图向上平面性的高效算法存在的首个障碍。我们还展示了相反方向的结果。假设将正整数多重集划分为两个和均为$n/2$的多重集可在$f(n)$时间内解决。令$G$为$n$顶点双连通外平面有向无环图，$e$为$G$的外平面画图中与外表面相邻的边。则判断$G$是否允许以$e$在外表面上的向上平面画图可在$O(f(n))$时间内完成。