On spanners of geometric graphsPublic Deposited
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Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every t with 1 1+1/t) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(tn1+2/(t+1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs.
- Gudmundsson, J. (Joachim), & Smid, M. (2006). On spanners of geometric graphs. doi:10.1007/11785293_36
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