Vector assignment problems: A general framework

We present a general framework for vector assignment problems, In such problems one aims at assigning n input vectors to m machines such that the value of a given target function is minimized. While previous approaches concentrated on simple target functions such as max-max, the general approach presented here enables us to design a polynomial time approximation scheme (PTAS) for a wide class of target functions. In particular, thanks to a novel technique of preprocessing the input vectors, we are able to deal with nonmonotone target functions. Such target functions arise in vector assignment problems in the context of video transmission and broadcasting.