An approximation algorithm for K-best enumeration of minimal connected edge dominating sets with cardinality constraints - Kurita, Kazuhiro; Wasa, Kunihiro (Theoretical computer science, 2024)
K-best enumeration, which asks to output k-best solutions without duplication, is a helpful tool in data analysis for many fields. In such fields, graphs typically represent data. Thus subgraph enumeration has been paid much attention to such fields. However, k-best enumeration tends to be intractable since, in many cases, finding one optimum solution is NP-hard. To overcome this difficulty, we combine k-best enumeration with a concept of enumeration algorithms called approximation enumeration algorithms. As a main result, we propose a 4-approximation algorithm for minimal connected edge dominating sets which outputs k minimal solutions with cardinality at most 4⋅OPT‾, where OPT‾ is the cardinality of a minimum solution which is not outputted by the algorithm. Our proposed algorithm runs in O(nm2Δ) delay, where n, m, Δ are the number of vertices, the number of edges, and the maximum degree of an input graph.