Abstract:A unit disk graph G on a given set of points P in the plane is a geometric graph where an edge exists between two points p, q ∈ P if and only if |pq| ≤ 1. A subgraph G of G is a k-hop spanner if and only if for every edge pq ∈ G, the topological shortest path between p, q in G has at most k edges. We obtain the following results for unit disk graphs.(i) Every n-vertex unit disk graph has a 5-hop spanner with at most 5.5n edges. We analyze the family of spanners constructed by Biniaz (WADS 2019) and improve the… Show more
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