Average case performance of heuristics for multi-dimensional assignment problems

We consider multi-dimensional assignment problems in a probabilistic setting. Our main results are: (i) A new efficient algorithm for the 3-dimensional planar problem, based on enumerating and selecting from a set of “alternating-path trees”; (ii) A new efficient matching-based algorithm for the 3-dimensional axial problem.

💡 Research Summary

The paper investigates the average‑case behavior of heuristics for multi‑dimensional assignment problems (MAP) in a probabilistic setting, focusing on two canonical 3‑dimensional variants: the planar (or “3‑dimensional planar”) problem and the axial (or “3‑dimensional axial”) problem. In the random model each entry of the cost tensor is drawn independently from a common distribution (typically Uniform