Reconfiguration of Multisets with Applications to Bin Packing

TL;DR

This paper introduces a general framework for reconfiguring multisets of items, with applications to bin packing, providing complexity results and algorithms for various scenarios, and exploring future research directions.

Contribution

It defines the Repacking problem for multisets, presents hardness results, and offers algorithms for specific instances, extending reconfiguration theory to new applications.

Findings

Hardness results for the general Repacking problem

Algorithms for specific classes of multiset reconfiguration

Connections to offline bin packing and future research avenues

Abstract

We use the reconfiguration framework to analyze problems that involve the rearrangement of items among groups. In various applications, a group of items could correspond to the files or jobs assigned to a particular machine, and the goal of rearrangement could be improving efficiency or increasing locality. To cover problems arising in a wide range of application areas, we define the general Repacking problem as the rearrangement of multisets of multisets. We present hardness results for the general case and algorithms for various classes of instances that arise in real-life scenarios. By limiting the total size of items in each multiset, our results can be viewed as an offline approach to Bin Packing, in which each bin is represented as a multiset. In addition to providing the first results on reconfiguration of multisets, our contributions open up several research avenues: the interplay between reconfiguration and online algorithms and parallel algorithms; the use of the tools of linear programming in reconfiguration; and, in the longer term, a focus on extra resources in reconfiguration.