The minimum directed feedback vertex set problem consists in finding the minimum set of vertices that should be removed in order to make a directed graph acyclic. This is a well-known NP-hard optimization problem with applications in various fields, such as VLSI chip design, bioinformatics and transaction processing deadlock prevention and node-weighted network design. We show a constant factor approximation for the directed feedback vertex set problem in graphs of bounded genus.

翻译：最小有向反馈顶点集问题旨在寻找从有向图中移除的最小顶点集，以使该图成为无环图。这是一个著名的NP难优化问题，在超大规模集成电路芯片设计、生物信息学、事务处理死锁预防及节点加权网络设计等多个领域具有应用。我们证明了在有界亏格图中，有向反馈顶点集问题存在常数因子近似算法。