Vector Bin Packing with Multiple-Choice

TL;DR

This paper introduces an approximation algorithm for multiple-choice vector bin packing, extending previous models to handle multiple item incarnations and bin types, with applications in network scheduling and other fields.

Contribution

It presents a novel approximation algorithm with a logarithmic factor for the cost, and a PTAS for the related multidimensional knapsack problem, expanding the scope of vector bin packing solutions.

Findings

Approximation algorithm with about ln D factor for multiple-choice vector bin packing.

Polynomial time complexity under certain dimensional and bin type constraints.

A PTAS for the multiple-choice multidimensional knapsack problem.

Abstract

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types, each with its own cost and $D$-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about $\ln D$ times the optimum. For the running time to be polynomial we require $D=O(1)$ and $T=O(\log n)$. This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin.