2002/07/16 by Jochen Alber, Alber, Jochen, Michael R. Fellows +3 · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #F.2.2 #FOS: Computer and information sciences #G.2.1 #G.2.2 #cs.DS
paper · pdf · doi:10.48550/arxiv.cs/0207066
25 pages, 4 figures (using 8 files), extended abstract entitled "Efficient Data Reduction for Dominating Set: A Linear Problem Kernel for the Planar Case" appeared in the Proceedings of the 8th SWAT 2002, LNCS 2368, pages 150-159, Springer-Verlag, 2002
arxiv created 2002/07/16 · openalex publication_date 2002/07/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy to implement reduction rules. Moreover, having implemented our reduction rules, first experiments indicate the impressive practical potential of these rules. Thus, this work seems to open up a new and prospective way how to cope with one of the most important problems in graph theory and combinatorial optimization.