We introduce a dynamic version of the NP-hard graph modification problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: having a cluster graph (that is, a disjoint union of cliques) constituting a solution for a first input graph, can we cost-efficiently transform it into a “similar” cluster graph that is a solution for a second (“subsequent”) input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (three modification scenarios edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as (parameterized) hardness results, thus (except for three open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the two perhaps most natural parameterizations: the distances of the new “similar” cluster graph to (1) the second input graph and to (2) the input cluster graph.

中文翻译：

---

参数化动态集群编辑

我们介绍了 NP-hard 图修改问题 Cluster Editing 的动态版本。这里的要点是考虑动态演化的输入图：具有构成第一个输入图的解决方案的集群图（即，不相交的集团联合），我们能否经济高效地将其转换为“类似”集群图是第二个（“后续”）输入图的解决方案？该模型受多种应用场景的启发，包括增量聚类、折衷聚类的搜索或基于图的数据聚类中的本地搜索。我们彻底研究了六个问题变体（三个修改场景边编辑、边删除、边插入；每个都结合了聚类图之间的两个距离度量）。