This chapter surveys approximation algorithms for hard geometric problems. The problems we consider typically take inputs that are point sets or polytopes in twoor three-dimensional space, and seek optimal constructions, (which may be trees, paths, or polytopes). We limit attention to problems for which no polynomial-time exact algorithms are known, and concentrate on bounds for worst-case approximation ratios, especially bounds that depend intrinsically on geometry. We illustrate our… CONTINUE READING