2014/10/31 by Jin-Hua Zhao, Yusupjan Habibulla, Haijun Zhou +1
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Complex Network Analysis Techniques #Computer science #Discrete mathematics #Dominating set #Greedy algorithm #Heuristic #Mathematical optimization #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Process (computing) #Set (abstract data type) #Statistical mechanics #Statistical physics #Stochastic processes and statistical mechanics #cond-mat.dis-nn #cs.CC #physics.soc-ph
paper · pdf · doi:10.1007/s10955-015-1220-2
published as Journal of Statistical Physics 159: 1154--1174 (2015) · Extensively revised (final version to be published in Journal of Statistical Physics). 19 pages in total
arxiv created 2015/02/05 · openalex publication_date 2015/02/20 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The minimum dominating set problem has wide applications in network science and related fields. It consists of assembling a node set of global minimum size such that any node of the network is either in this set or is adjacent to at least one node of this set. Although this is a difficult optimization problem in general, we show it can be exactly solved by a generalized leaf-removal process if the network contains no core. If the network has an extensive core, we estimate the size of minimum dominating sets by a mean-field theory and implement a belief-propagation algorithm to obtain near-optimal solutions. Our algorithms also perform well on real-world network instances.