Introduction to Best-Packing and Best-Covering
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In this chapter we discuss two fundamental problems of discrete geometry, the best-packing problem and the best-covering problem. In Section 3.1 the general best-packing problem is introduced. We show that it is the limiting case as \(s\rightarrow \infty \) of the Riesz s-energy problem, see Proposition 3.1.2. In that section we also estimate the minimal pairwise separation of an N-point s-energy minimizing configuration on a path connected compact set. Section 3.2 introduces the general best-covering problem and discusses the basic relationship between best-packing distance and mesh ratio on a given compact set.