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应移除的最小顶点集，以使有向图成为无环图。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、事务处理死锁预防以及节点加权网络设计等多个领域均有应用。我们提出了有界亏格图中最小有向反馈顶点集问题的常数因子近似算法。