Nonlinear Assignment Problems pp 1-12 | Cite as

# Multi Index Assignment Problems: Complexity, Approximation, Applications

## Abstract

This chapter deals with approximation algorithms for and applications of multi index assignment problems (MIAPs). MIAPs and relatives of it have a relatively long history both in applications as well as in theoretical results, starting at least in the fifties (see e.g. [Motzkin, 1952], [Schell, 1955] and [Koopmans and Beckmann, 1957]). Here we intend to give the reader i) an idea of the range and diversity of practical problems that have been formulated as an MIAP, and ii) an overview on what is known on theoretical aspects of solving instances of MIAPs. In particular, we will discuss complexity and approximability issues for *special cases* of MIAPs. We feel that investigating special cases of MIAPs is an important topic since real-world instances almost always posses a certain structure that can be exploited when it comes to solving them.

## Keywords

Assignment Problem Polynomial Time Approximation Scheme Assignment Game Discrete Apply Mathematic Multidimensional Assignment Problem## Preview

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