On generic NP-completeness of the graph clustering problem
Alexander Rybalov · Journal of Physics Conference Series · 2020
Abstract Generic-case approach to algorithmic problems was suggested by Miasnikov, Kapovich, Schupp and Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the problem of clustering graphs. In this problem the structure of relations of objects is presented as a graph: vertices correspond to objects, and edges connect similar objects. It is required to divide a set of objects into disjoint groups (clusters) to minimize the number of connections between clusters and the number of missing links within clusters. We prove that the graph clustering problem is NP-hard with respect to generic analog of polynomial Turing reduction. Supported by Russian Science Foundation, grant 18-71-10028.