EPTAS for the dual of splittable bin packing with cardinality constraint

TL;DR

This paper presents an Efficient Polynomial-Time Approximation Scheme (EPTAS) for the dual of splittable bin packing with a cardinality constraint, addressing an open problem in the field.

Contribution

The paper introduces an EPTAS for the dual splittable bin packing problem with variable cardinality, solving an open question in the literature.

Findings

EPTAS achieves near-optimal solutions efficiently.

Addresses an open problem in bin packing theory.

Applicable when the cardinality constraint is part of the input.

Abstract

The problem considered is the splittable bin packing with cardinality constraint. It is a variant of the bin packing problem where items are allowed to be split into parts but the number of parts in each bin is at most a given upper bound. Two versions of the splittable bin packing with cardinality constraint have been studied in the literature. Among these variants we consider the dual one where the objective is to minimize the maximum bin size while packing (may be fractional) the items to a given set of bins. We exhibit an EPTAS for the dual problem when the cardinality upper bound is part of the input. This result answers an open question raised by Epstein, Levin, and van Stee.