We study the problem of determining the minimal genus of a given finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices, determines the orientable genus of $G$ in $\mathcal{O}({2^{(n^2+3n)}}/{n^{(n+1)}})$ steps. This algorithm avoids the difficulties that many other genus algorithms have with handling bridge placements which is a well-known issue. The algorithm has a number of properties that make it useful for practical use: it is simple to implement, it outputs the faces of the optimal embedding, it outputs a proof certificate for verification and it can be used to obtain upper and lower bounds. We illustrate the algorithm by determining the genus of the $(3,12)$ cage (which is 17); other graphs are also considered.

翻译：我们研究了确定给定有限连通图的最小亏格问题。本文提出一种算法，对于具有$n$个顶点的任意图$G$，可在$\mathcal{O}({2^{(n^2+3n)}}/{n^{(n+1)}})$步骤内确定$G$的可定向亏格。该算法避免了其他许多亏格算法在处理桥接配置时遇到的困难——这是一个众所周知的问题。本算法具有若干适合实际应用的特性：易于实现、可输出最优嵌入的面结构、可生成供验证的证明凭证，并能用于获取上下界。我们通过确定$(3,12)$笼图（其亏格为17）的亏格来演示算法；文中也考察了其他图例。