This paper addresses the connected maximum coverage problem, motivated by the detection of mutated driver pathways in cancer. The connected maximum coverage problem is NP-hard and therefore approximation algorithms are of interest. We provide here an approximation algorithm for the problem with an approximation bound that strictly improves on previous results. A second approximation algorithm with faster run time, though worse approximation factor, is presented as well. The two algorithms are then applied to submodular maximization over a connected subgraph, with a monotone submodular set function, delivering the same approximation bounds as for the coverage maximization case.

本文探讨了由于检测到癌症中突变的驱动程序通路而导致的最大连接覆盖率问题。连接的最大覆盖范围问题是NP难的，因此近似算法很重要。我们在这里为问题提供了一种近似算法，其逼近界限严格地改善了先前的结果。还提出了具有更快运行时间的第二近似算法，尽管近似因子较差。然后将这两种算法应用于具有单调子模集功能的连接子图上的子模最大化，从而提供与coverage最大化情况相同的逼近范围。