We study the problem of determining the minimal genus of a simple finite connected graph. We present an algorithm which, for an arbitrary graph $G$ with $n$ vertices and $m$ edges, determines the orientable genus of $G$ in $O(n(4^m/n)^{n/t})$ steps where $t$ is the girth of $G$. This algorithm avoids difficulties that many other genus algorithms have with handling bridge placements which is a well-known issue. The algorithm has a number of useful properties for practical use: it is simple to implement, it outputs the faces of an optimal embedding, and it iteratively narrows both 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：我们研究了确定简单有限连通图最小亏格的问题。本文提出一种算法，对于具有$n$个顶点和$m$条边的任意图$G$，该算法能以$O(n(4^m/n)^{n/t})$步数确定$G$的可定向亏格，其中$t$为$G$的围长。该算法避免了其他许多亏格算法在处理桥接放置这一已知难题时面临的困难。该算法具有若干实用特性：易于实现，可输出最优嵌入的面结构，并能迭代收窄上下界。我们通过确定$(3,12)$笼形图（亏格为17）以及其他图例说明了该算法的有效性。