2008/11/14 by Richard J. Mathar, Mathar, Richard J. · 1 citation
Engineering · Mathematics · #05C90 #51M04 #52C05 #52C15 #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:05C90 #msc:51M04 #msc:52C05 #msc:52C15
paper · pdf · doi:10.48550/arxiv.0811.2434
20 pages, 18 figures
arxiv created 2008/11/14 · openalex publication_date 2008/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Each straight infinite line defined by two vertices of a finite square point lattice contains (covers) these two points and a - possibly empty - subset of points that happen to be collinear to these. This work documents vertex subsets of minimum order such that the sum of the infinite straight lines associated with the edges of their complete subgraph covers the entire set of vertices (nodes). This is an abstraction to the problem of sending a light signal to all stations (receivers) in a square array with a minimum number of stations also equipped with transmitters to redirect the light to other transmitters.