Efficiently enumerating all the extreme points of a polytope identified by a system of linear inequalities is a well-known challenge issue.We consider a special case and present an algorithm that enumerates all the extreme points of a bisubmodular polyhedron in $\mathcal{O}(n^4|V|)$ time and $\mathcal{O}(n^2)$ space complexity, where $ n$ is the dimension of underlying space and $V$ is the set of outputs. We use the reverse search and signed poset linked to extreme points to avoid the redundant search. Our algorithm is a generalization of enumerating all the extreme points of a base polyhedron which comprises some combinatorial enumeration problems.

翻译：高效枚举由线性不等式系统确定的凸多面体所有极点是一个众所周知的难题。本文研究一种特殊情况，提出一种算法，可在 $\mathcal{O}(n^4|V|)$ 时间复杂度和 $\mathcal{O}(n^2)$ 空间复杂度内枚举双模多面体的所有极点，其中 $n$ 表示底层空间的维度，$V$ 为输出集合。我们采用逆向搜索策略并结合与极点关联的符号偏序集来避免冗余搜索。该算法是基多面体极点枚举方法的推广，涵盖若干组合枚举问题。