Partition in high dimensional spaces

Partition combined with shifting strategy is a powerful method in producing polynomial time approximation scheme (PTAS) for many NP-hard geometric problems. The focus of this chapter is on the ideas and the techniques of partition method which can be applied to high dimensional space, including the basic ideas, the small compensation technique which is used to deal with the requirement of connection, the multilayer partition technique which is used to deal with the situation when the geometric objects are not uniform, and the growing partition technique which does not require the geometric representation of the graph.

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