Gábor Galambos

Bin Packing Approximation Algorithms: Combinatorial Analysis

In the classical version of the bin packing problem one is given a list L = (a 1,...,a n ) of items (or elements) and an infinite supply of bins with capacity C. A function s(a i ) gives the size of item a i , and satisfies 0 < s(a i )≤C, 1 ≤ i ≤ n. The problem is to pack the items into a minimum number of bins under the constraint that the sum of the sizes of the items in each bin is no greater than C. In simpler terms, a set of numbers is to be partitioned into a minimum number of blocks subject to a sum constraint common to each block. We use the bin packing terminology, as it eases considerably the problem of describing and analyzing algorithms.

An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling

The problem of on-line scheduling a set of independent jobs on m machines is considered. The goal is to minimize the makespan of the schedule. Graham’s List Scheduling heuristic [R. L. Graham, SIAM J. Appl. Math., 17(1969), pp. 416–429] guarantees a worst case performance of

New lower bounds for certain classes of bin packing algorithms

2 - \frac{1} {m}

On-line bin packing — A restricted survey

for this problem. This worst case bound cannot be improved for

Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem

m = 2

Repacking helps in bounded space on-line bind-packing

and

An exact algorithm for scheduling identical coupled tasks

m = 3

Lower bounds for 1-, 2- and 3-dimensional on-line bin packing algorithms

. For

Lower Bound for the Online Bin Packing Problem with Restricted Repacking

m \geqslant 4

A simple proof of Liang's lower bound for on-line bin packing and the extension to the parametric case

, approximation algorithms with worst case performance at most