 
Summary: Online BinStretching \Lambda
Yossi Azar y Oded Regev z
Abstract
We are given a sequence of items that can be packed into m unit size bins. In the
classical bin packing problem we fix the size of the bins and try to pack the items in
the minimum number of such bins. In contrast, in the binstretching problem we fix
the number of bins and try to pack the items while stretching the size of the bins as
least as possible. We present two online algorithms for the binstretching problem that
guarantee a stretching factor of 5=3 for any number m of bins. We then combine the
two algorithms and design an algorithm whose stretching factor is 1:625 for any m.
The analysis for the performance of this algorithm is tight. The best lower bound for
any algorithm is 4=3 for any m – 2. We note that the binstretching problem is also
equivalent to the classical scheduling (load balancing) problem in which the value of the
makespan (maximum load) is known in advance.
Keywords. Online algorithms, approximation algorithms, binstretching, load bal
ancing, scheduling, binpacking.
1 Introduction
The online binstretching problem is defined as follows. We are given a sequence of items
that can be packed into m bins of unit size. We are asked to pack them in an online fashion
minimizing the stretching factor of the bins. In other words, our goal is to stretch the sizes
